Supporting Information Modha and Singh SI Text Transpose of Themselves, Brain Regions with Different Acronyms but the Largest Previous Network

Supporting Information Modha and Singh SI Text transpose of themselves, brain regions with different acronyms but The Largest Previous Network. The largest previous network of the with the same full name, typographical errors, incorrect case, miss- macaque brain consists of 95 vertices and 2,402 edges [1], where the ing special characters, existence of brain regions without mapping network models brain regions as vertices and the presence of long dis- or connectivity relations, incorrect L and I relations, self-loops in L tance connections as directed edges between them. This network is relation, missing relations, and so on. displayed in Figure S1 and should be compared to our network in Fig- ure 1 of the main text. It can be seen that the largest previous network Constructing a Network and a Hierarchical Brain Map. Let us rep- completely misses corticosubcortical and subcortico-subcortical long resent mapping relations I, L, O, E, C and the connectivity rela- distance connections and has significant gaps even amongst cortico- tion CNZ as two-dimensional binary matrices. The rows as well as cortical long distance connections. Two-thirds of our data has never columns correspond to various brain regions. The (i, j)-th entry of even been previously compiled, let alone analyzed and understood. I relation is 1 if there exists an identity relation between the brain regions corresponding to row i and column j, and zero otherwise. CoCoMac Database. We briefly summarize the CoCoMac database, Similarly, for L, O, E, C matrices the (i, j)-th entry is 1 if there ex- and refer the reader to the original publications for more details ists the associated relation between the brain regions corresponding [2, 3, 4, 5, 6]. CoCoMac consists of three primary databases: lit- to row i and column j. For CNZ matrix, 1 denotes the presence of a erature, mapping, and connectivity. connection between brain regions of corresponding row and column. From a matrix-theoretic view point, merging a pair of brain regions • Each included literature study is assigned a unique identifier, i and j amounts to, for each of the six matrices, computing a logi- LitID. For example, the paper by Pandya and Seltzer in 1982 [7] cal OR of their respective rows and columns, updating the respective is referred to as PS82. rows and columns by the ORed value, and removing one each of the • A BrainMap is a parcellation or mapping scheme used in a par- rows and columns, thus reducing the numbers of rows and columns ticular study. A BrainMap is also referred to using LitID.A by one. At any time, only a binary (zero or non-zero) entry is main- particular study may define and use a new BrainMap or it may tained for each of the matrices. use a previously defined map by another study. Thus, there are We now give a brief description of our data processing pipeline, a fewer BrainMaps than LitIDs. series of manual and algorithmic data transformations that transform A BrainMap is a set of BrainRegions, where a brain region initial matrices of size 6,877 × 6,877, into compact final matrices of refers to cortical and subcortical subdivisions (area, region, nu- size 383 × 383. At the end, I, E, and C become identity matrices, L cleus, etc.) as well as to combinations of such subdivisions into becomes the adjacency matrix of our hierarchical brain map, and the sulci, gyri, and other large ensembles1. A brain region is uniquely final CNZ has 6,602 non-zero entries – the edges of our network. identified as a concatenation of the BrainMap that it belongs to In the initial matrices, the connectivity information is scattered and its Acronym, that is, as LitID-Acronym. For example, V1 across brain regions, literature studies, and parcellation schemes. in FV91 [8] is uniquely referred to as FV91-V1 whereas V1 in This information has to be pieced together because: RD96 [9] is uniquely referred to as RD96-V1. BrainRegion Further, various s are related to each other via six 1. Different studies performed at different times by different groups identity I sub-structure S logical mapping relations, namely, ( ), ( ), by using different techniques on different animals and at differ- supra-structure L overlapping structure O expanded ( ), and ( ), ent resolutions, inevitably lead to a wide variety of nomenclature lamina (E), and collapsed lamina (C). • and parcellation schemes. For example, connectivity information Connectivity database consists of a set of records representing for primary visual area is scattered across 42 different reports that BrainRegion directed long distance connections from a source study V1, 15 different reports that study brain region 17, and 6 BrainRegion to a target . Further, each connection is annotated different reports that study StriateC. by experimentally determined strength: 1 for weak/sparse, 2 for 2. Without aggregating connectivity information of equivalent brain moderate, 3 for strong/heavy, X for unspecified density, and 0 for regions, one would only see disconnected path fragments. This absence of tested projection. point is illustrated in Figure S2 that shows how establishing equivalences between identical brain regions and then merging them Statistics of Downloaded Databases. When downloading the is essential to uncovering reciprocal connections or to uncover a database, we have ignored the fields PDC, Ref.text, and Ref.fig. short circular loop. We now enumerate gross statistics of the downloaded database. 3. Merging of equivalent brain regions is essential for network anal- • 410 unique LitIDs (literature studies) ysis. For example, the shortest path between two regions captures • 379 unique BrainMaps (parcellation schemes) the degree of coupling between them. The longest shortest path in • 6,877 unique BrainRegions the network captures the extremum over all pairs, and is known as • 1,880 unique Acronyms the diameter. Without merging, the brain’s connectivity appears • 10,681 unique, directed connections from one BrainRegion to significantly sparser than it actually is, for example, the diam- another with density labels “1”, “2”, “3”, or “X” eter appears dramatically larger, namely, 13, than it actually is, • 13,498 unique records showing tested but not found connections namely, 6. between a pair of BrainRegions with density label “0” • 16,712 unique records interrelating BrainRegions to each other: Consequently, in order to obtain a complete and correct picture of 9,134 I relations, 3,185 L relations, 3,185 S relations, 662 O rela- the brain’s connectivity, it is imperative that brain regions that are tions, 272 E relations, and 272 C relations. identical are merged into a single region. We now formalize the key difficulty in merging. Define conflict The downloaded database had a number of errors that had to be cor- relation as the intersection, logical conjunction, of I and L. In other rected, for example, incorrect associations between acronyms and words, conflict happens when two regions are identified both via the brain regions, lack of acronym field in the connectivity database, the supra-structure relation L not being the symmetric transpose of substructure relation S, the relations I and O not being the symmetric 1CoCoMac refers to BrainRegion as BrainSite.

1 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh identity and superstructure relations. For example, the database con- children. In both of these cases, the resolution is not useful for contains statements: FEF and 8A are identical and that FEF is a super- nectivity studies, and is sacrificed for the sake of conciseness, and structure of 8A. The relations I and L are transitive [4]. So, if A is the regions are merged. Further, from the view point of connectiv- identical to B, and B is identical to C, then A is implied to be iden- ity analysis, the resulting parcellation has the pleasing property that tical to C. The space of all implied identity and superstructure rela- every leaf brain region has two-way connectivity. Throughout, we tions are captured by their respective transitive closures I+ and L+. preserved every single connectivity datum with care except that we In matrix-theoretic parlance: I+ = I ∨ I2 ∨ ..., where ∨ represents removed all direct self-loops and all indirect self-loops in the form OR or logical disjunction. It should be noted that I+ and L+ contain of connections between a brain region and its ascendants or descen- a combinatorial large number of entries. We now extend the defi- dants (where ascendants and descendants are defined with respect to nition of conflict relation to mean the intersection between I+ and the above hierarchical brain map). L+. Conflicts arising because of transitivity are far too numerous, For overlap relation O, note that there are 9,134 I relations and are inherently insidious, and are extremely difficult to track and to 3,185 L relations, but only 662 O relations in CoCoMac. The sym- eliminate (see Figure S3). metry implies that there actually only 331 O relations. The impact of We highlight an interesting sub-routine inspired by ORT[3, Ap- overlap is mitigated due to the following reasons, pendix E] that we have repeatedly used for merging. The idea is to + + 1. Thinking of I, L, O as binary set relations, overlap is a weaker computes a submatrix J of I such that intersection of J and L is relationship than subset which in turn is weaker than identity. As empty. Then, J is a conflict-free identity relation, and can be safely a result, 112 O relations are subsumed by I and 26 relations are used for merging. This is pictorially described in Figure S4 2. Our subsumed by L. goal is to derive a CNZ for network analysis, with emphasis being on 2. Even if there is overlap between brain regions in mapping relation, merging equivalent brain regions. Towards that our relation J has a there is often no overlap in connectivity which further mitigates number of desirable properties. Specifically, even after merging with any effect of overlaps. This subsumes 50 more O relations. J, each brain region can be uniquely identified with one and only one of the merged brain regions. If two original brain regions had Net, only 143 O relations are present in our final data. Two arbitrary a L relationship before merging, then the relationship is preserved brain regions have, on an average, 96% distinct connections, while amongst the merged regions. Further, J is such that no two equiva- brain regions involved in the 143 overlap relations have, on an av- lence classes of brain regions can be further merged without creating erage, 79% distinct connections. Thus, even if there is overlap in a conflict. Our algorithm greedily computes such a J and stops when mapping and connectivity, the overlapping regions have substantially conflicts are detected. On detection we can either use the computed J different connectivity and whether they can be merged is debatable. to merge the set of brain regions, or examine the conflict3. In certain We visualize the 143 O relations in Figure S5. Despite ignoring the cases, the conflict is resolved manually using the slice-based atlas O relationship, we find that most remaining O relationships lie close of the Rhesus monkey cortex [10]. This lends a physical constraint to the diagonal for a depth first order scan of our brain map. Conse- to the logical processing described above. Throughout the merging quently, overlap is mostly between siblings or cousin vertices in the process, we ensure that two brain regions within a literature study hierarchy, or between regions like 25 and 14 that are known to be are never merged unless they are explicitly identified as equivalent. adjacent on the cortex. This ensures that every parcellation originally present in CoCoMac In summary, merging equivalent brain region is imperative for is represented in our data. network-analysis. It is interesting to note that 93% of the original I It is desirable to organize merged brain regions into a coherent, relations are respected in our hierarchical brain map, that is the corre- unified hierarchical brain map. A hierarchical brain map provides a sponding brain regions are merged. The hierarchy that we obtain is at natural frame of reference to place, understand, and correlate various the highest resolution that the data can meaningfully support. Given brain regions. For network analysis, a hierarchical brain map pro- a set of merged regions, the hierarchy is invaluable for visualization vides a tool to vary the resolution of network, to analyze aggregate (Figure S6 and the derivative figures) and for aggregate connectivity connectivity patterns. For example, without a hierarchical brain map, analysis (Tables S2 and S3), but does not play a role in network- we can observe that V4 connects to TF, but cannot answer how many analysis. total connections are made between occipital lobe and temporal lobe. The final set of merged regions and the hierarchical brain map The key difficulty in defining a unified hierarchical brain map is that are visualized in Figure S6 and described in Table S1 for complete underlying L relation is a directed acyclic graph (not a tree) and con- transparency. tains multiple disjoint components. The key steps that we have taken to overcome this are: Hierarchical Brain Map.The final resulting parcellation has 383 unique, hierarchically organized, merged brain regions. The entire 1. Removed redundancy and simplified L. Specifically, if A is a su- set of merged brain regions and the complete parcellation are explic- perstructure of B, then all superstructure relations from A to any itly detailed in the multi-page Table S1 to provide transparency and descendants of B are removed. This is done repeatedly through 4 to permit future additions as data with finer resolution becomes avail- the pipeline . able. We explain the table: 2. Used a number of existing brain maps from CoCoMac, underlying literature, and existing atlases, for example, GM (a brain 1. The first column shows “Level” of a node with respect to this map based on conceptual relationships), R00 (a topographical re- parcellation, where, the root node “Br” (brain) has level 0, its im- gional map), and the slice-based atlas of the Rhesus monkey cor- mediate children (DiE, Cx, BG, MB#2, OFC) have level 1, and tex [10, 11]. their immediate children have level 2, and so on. 2. For each set of merged brain regions, one of the merged regions As pre-processing, we merged all laminae into their respective was chosen manually to represent the entire set. The second col- brain regions (using relations E and C), merged all brain regions with umn shows the Acronym corresponding to the chosen represen- the same Acronym, and removed all cycles from L ensuring that it tative brain region which is used to label the entire set. To ensure is a directed acyclic graph. As main processing steps, we merged the equivalent brain regions and placed them in a coherent parcellation. As post-processing, we merged pairs of (non-equivalent) brain re- 2 J can be considered to be a valid path in the transform graph of ORT[3, Figure 5, Appendix gions such that one is a child of another if (a) the child is a leaf in the E]. We make the simplifying assumption of not using O relation, see discussion below. 3In contrast ORT uses PDC, manually inserted labels coding the precision of descriptions, to overall parcellation and the child does not have two-way connectiv- find the optimal valid path in the transformation graph. ity (that is both to- and from-) or if (b) the parent region has no other 4A, B represents sets of merged brain regions

2 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh consistent nomenclature, we have simply carried the Acronyms along the hierarchy, that is, the shortest number of hops required to over from CoCoMac. It is important to note that there is a one-to- travel from the vertex to the root. Note that this distance corresponds one correspondence between a vertex in the network and a repre- exactly to the first column in Table S1. On one hand, conventional sentative brain region. radial tree layout naturally captures the hierarchy. On the other hand, 3. The third column shows the full name of the representative brain for large hierarchies, the leaf vertices tend to overlap rendering the region that has also been carried over from CoCoMac. Within labels unreadable [13]. square brackets, the third column also shows the Acronyms of the Conventional tree layout algorithm starts with the root at the cen- brain regions that have been merged into the representative brain ter and works radially outwards according to the inherent hierarchy. region. For example, 17, 17 I, LVQ, OC, StriateC, StriateC-I, We now describe a novel, alternate radial tree layout algorithm that StriateC-II, StriateC-III, StriateC-IV, UVQ, V1 I, V1 II, V1 III, starts with the leaves at a common periphery and works radially in- have all been merged in V1. To avoid unnecessary clutter, if a wards. brain region is merged, but had no connectivity information asso- 1. Compute shortest path from every vertex to the root. ciated with it, then it is not shown within the square brackets. 2. From these shortest paths, determine the length of the longest 4. The hierarchical brain map is displayed in Figure S6. The figure shortest path, say, L. Note that L = 9 for our hierarchy. contains one center and 11 concentric rings. The center is as- 3. Traverse the hierarchy in a breadth-first fashion. As the leaf ver- signed the number 0, the innermost ring is assigned the number 1, tices are encountered by this traversal, assign to them ring num- and outer rings are assigned a progressively larger number. Each bers in a round-robin manner: L, L + 1, ..., L + k, L, L + 1, brain region resides on one of these rings, and the fourth column ..., L + k, and so on. Note that in our experiments, we found that of the table displays the corresponding ring number for each brain k = 2 leads to sufficient spacing between the leaf vertices. region. 4. Recursively, for every non-leaf vertex, assign to it the ring num- 5. The fifth column shows the total number of edges that the vertex ber that is one less than the minimum ring number assigned to its (corresponding to the brain region) touches in the long distance children. network shown in Figure 1 of the main text. 6. The sixth column shows how often the set of merged brain regions This ring numbering algorithm will naturally assign the number zero have been have been studied in the literature reports compiled by to the root. Once again, the root of the hierarchy, is placed at the CoCoMac. center of the display, and all the other vertices are arranged on con- 7. The seventh column shows the number of unique connections centric rings around it. Each vertex lies on the ring corresponding to (with density labels “1”, “2”, “3”, and “X”) reported for the set its ring number. When applied to our hierarchy, this algorithm leads of merged brain regions in the literature reports compiled by Co- to Figure S6. A disadvantage of Figure S6 is that the ring numbers do CoMac. not correspond to the hierarchical levels. We compensate for this by listing both the ring numbers and the hierarchical levels in Table S1. Dataset. The dataset consists of three text files: On the advantages, it can be seen that the leaf vertices do not occlude one another and peripheral space is efficiently used. This maximizes 1. Macaque LongDistance Network.nameslist: 2 column text file. the amount of white space in the center which we utilize to effectively The first column is a numerical index and second column is display the brain network in Figure 1 of the main text. the Acronym string of the corresponding brain region. The Acronym of brain regions are listed in the second column of Ta- Visualizing the Hierarchical Brain Map: Effective use of Color. ble S1. There are 383 rows corresponding to the 383 brain regions “It is not the form that dictates the color, but the color that in our network. The brain regions are ordered identically in the brings out the form.” Hans Hofmann data file and in Table S1. 2. Macaque LongDistance Network connectivity.edgelist: 2 col- The symmetry and circularity of alternate radial tree layout nat- umn text file. Each row corresponds to a directed edge in the net- urally evokes an analogy with the color wheel. We color the vertices work between a source brain region and a target brain region. The of the hierarchical brain map based on the HSV color wheel [14]. first column is the index of the source brain region and the second For even better discrimination amongst the leaf vertices, we rotate column is the index of the target brain region, where the indices the color wheel by 120 degrees for the second outermost ring, and by are from Macaque LongDistance Network.nameslist. There are 240 degrees for the outermost ring. Further, we have used black text 6602 rows corresponding to the nonzero entries in CNZ. color throughout for labeling individual vertices. Figure S6 as well 3. Macaque LongDistance Network mapping.edgelist: 2 column as all our figures, unless noted otherwise, use this default coloring text file. Each row corresponds to a parent-child relationship template. As can be seen, color vibrantly affects presentation [15]. in our hierarchical brain map. The first column is the in- Accessibility is an important criteria for drawing large hierar- dex of the parent brain region and the second column is the chies such as ours. Given the small font size that the limited page index of the child brain region, where the indices are from size imposes, the accessibility is a particular concern in regards to Macaque LongDistance Network.nameslist. There are 382 rows the text labels used to annotate each vertex in the hierarchy. Black corresponding to the nonzero entries in L. text in our default coloring template is harder to discern on darker background, especially, dark blue. We provide two alternate methods to enhance accessibility. Visualizing the Hierarchical Brain Map: Efficient use of Space. Our brain map is a large, unbalanced hierarchy, and effectively visualiz- 1. For higher-resolution, easier-to-read access to the hierarchy, we ing it within the confines of a two-dimensional page is a tremendous zoom into various sub-structures of Figure S6 in Figures S7, S8, challenge. We explored how to effectively use space to make the S9, S10, S11, S12, S13, and S14. hierarchy understandable and accessible to a wide audience. 2. For improving the contrast between foreground text labels and Radial tree is often used to layout hierarchies [12]. In this layout background color, we provide an alternative to Figure S6. Specif- a single vertex, namely, the root of the hierarchy is placed at the cen- ically, we use white foreground with dark background, and black ter of the display, and all the other vertices are arranged on concentric foreground with light background in Figure S15. rings around it. The center is assigned the number 0, the innermost ring is assigned the number 1, and outer rings are assigned a progres- Visualization of the Long Distance Network. Using the brain regions sively larger number. In a conventional radial tree layout, each vertex in the hierarchical brain map as vertices, we extract a network con- lies on the ring corresponding to its shortest distance from the root taining 6,602 edges wherein an edge encodes the presence of long

3 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh distance connection between corresponding brain regions. Drawing Six Degrees of Separation. The shortest path between two regions each edge as a straight line between the two terminal vertices leads captures the degree of coupling between them. The longest short- to a highly cluttered visualization where no details are discernible, est path in the network captures the extremum over all pairs, and is as shown in Figure S17(a). Consequently, for clarity, an innovative known as the diameter. For the SCC, quite surprisingly, the diameter approach is needed to reduce cluster while still preserving as much is actually 6, exactly! Thus, the brain has the proverbial six degrees information as possible. of separation [20], and the “gossip” about every brain region’s activ- One of the ways to reduce clutter is to bundle similar edges some- ity spreads to every other region within the SCC in six hops or less. how. We employ the award-winning hierarchical edge bundling algo- Diameter of corticocortical network is even smaller, namely, just 5. rithm proposed by Danny Holten [16]: Small World Networks. The average shortest path between any two “Hierarchical edge bundling is based on the principle of visu- pairs of vertices is known as the characteristic path length (L). The ally bundling adjacency edges together analogous to the way average fraction of allowable edges between neighbors of any region electrical wires and network cables are merged into bundles that actually exist is known as the average clustering coefficient (C). along their joint paths and fanned out again at the end, in order Random networks are characterized by small values of L and C, to make an otherwise tangled web of wires and cables more while regular networks are characterized by large values of L and manageable.” C. For the SCC, we have that L = 2.62 which is small compared to a regular network and that C = 0.33 which is high compared Suppose that we are trying to render an edge in the long distance to a random network (C = 0.0528, 100 trials). The brain is nei- network from a source vertex to a destination vertex. To this end, our ther completely random nor completely regular. Rather, these values hierarchical brain map can be used as a natural scaffold as in [16]. of L and C imply that even our comprehensive and colossal long 1. Compute the path along the hierarchy from each of these two ver- distance brain network is small-world [21, 22]. Dynamically small- tices to the central root vertex (Br). world networks are characterized by “enhanced signal-propagation 2. Define the lowest common ancestor as that vertex at which these speed, computation power, and synchronizability” [21] all proper- paths first meet. ties clearly manifested in the brain. What separates the brain net- 3. Define a hierarchical path between two vertices as a path from work from a random network is its inherent clustering and complex- the source vertex to the lowest common ancestor vertex, and from ity [23, 24]. the lowest common ancestor vertex to the destination vertex. 4. Render a spline curve using this hierarchical path as the control Complex System. By using hierarchical relation between brain re- polygon. The spline curve is then used to visualize the edge be- gions, it is now possible for us to study not just individual connec- tween the two vertices, instead of the direct line connecting the tions between pairs of brain regions, but rather aggregate connections two vertices. between any two larger sub-structures as well. Such aggregation can 5. The spline rendering algorithm uses a bundling factor β, 0 ≤ β ≤ be performed at many different levels of hierarchy representing dif- 1, that controls how close the spline curve is to the control poly- ferent resolutions, for example, temporal lobe may studied at a finer gon. Higher β implies more closeness and, consequently, more granularity or various cortical constituents can all be combined to bundling between splines having common control polygon points. permit a coarser perspective. This permits a deeper analysis and understanding of how different structures and sub-structures connect The bundling process and the effect of the bundling factor β are il- and interact with each other, see, for example, Table S2 for a sum- lustrated via an example in Figure S16 and via the whole network in mary view of corticocortical and corticosubcortical systems. It can Figure S17. It can be seen that as bundling factor increases, clutter be seen Cx is heavily connected with itself, whereas DiE and BG are decreases, and structure emerges. heavily connected with Cx. Having constructed and visualized our network, we now proceed Further refining Table S2, in Table S3, we summarize the number to analyze it. of connections in major corticocortical and corticosubcortical pathways by dividing Cx into its six constituents: TL#2, FL#2, Pl#6, Classical Fiber Systems. The visual system [8], the dorsal-ventral OC#2, Insula, and CgG#2. Such a precise quantitative perspective on pathways [17], thalamocortical relays [18], and numerous cortico- interactions between various brain sub-structures has not been previ- cortical, corticosubcortical, and subcortico-subcortical fiber systems ously possible. Table S3 contains a number of interesting insights, [19] serve as the very basis of our understanding of white matter as examples, observe that cingulate cortex is very tightly intercon- pathways in the brain. Table S4 enumerates brain regions involved nected with frontal lobe, that frontal lobe has the highest average in these fiber systems. Comprehensiveness of our network is under- in-degree amongst all enumerated structures, and that a region in in- scored by the fact that it contains logical sub-networks corresponding sula sends out, on an average, two connections for every connection to all these physical fiber systems as demonstrated in Figures S18, that it receives. Further, various cortical constituents are highly in- S19, S20, and S21. terconnected and are also intertwined with diencephalon (DiE) and basal ganglia (BG). A divide-and-conquer approach to studying each Strongly Connected Component. For our network, only 4.5% of the constituent part in isolation by ignoring the interrelationships is un- possible connections exist, so the network is sparse. A large fraction likely to be fruitful. The brain is truly a complex system for inte- of connections, namely, 42%, are reciprocal. Out of 383 regions, 351 grating information that is substantially more than a simple sum of regions have both efferent and afferent connectivity and these form its parts, and thus must be studied as a whole. The behavior of the a strongly connected component (SCC) such that each such region is brain apparently emerges via non-random, correlated interactions be- reachable from every other. Six regions have only efferent connec- tween parts, which is a key characteristic of organized complexity tions to the SCC, three regions have only afferent connections from [26]. Such complex systems are often amenable to computer model- the SCC, and the remaining 23 regions have no connections and con- ing and simulation thus pointing to a prosperous future for computa- sist of big container regions, for example, cortex (Cx), diencephalon tional neuroscience. (DiE), basal ganglia (BG), etc., that are required to hold the hierarchy together. The SCC contains 6,491 connections (roughly 98.32%), Computing k-Cores. Suppose that we are given an undirected graph and its surprisingly large size implies that the brain invests tremen- with vertex set V and edge set E. For k ≥ 1, a k-core is the maximal dous communication resources in talking to and listening to itself. subset Vk of V such that every vertex in Vk has at least k connections Within the SCC, the average in- and out-degrees are both 18.81. with other vertices in Vk. The cores are recursively computed as fol-

4 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh lows. Set V0 = V . Now, to obtain Vk, k ≥ 1, start from Vk−1 and area 19) roughly map, assuming homology between human-macaque while there remain any vertices with less than k connections remove [29, 30, 31, 32, 33, 34], to 7#1, 7b, 7a, IPL, PF#1, PG#1, S2, 2#1, ˆ STS, TPO, TPOc, 6#1, 6D, 6M, 6V, F2, F7, F6, F3, SMAr, F4, F5, them. The process stops at some k ≥ 1 such that Vkˆ+1 = ∅. In- creasing k amounts to recursively peeling off the underlying network PrCO, 46, 46d, 46v, PS, Ig#1, Idg, Ia#2, Iai, Iam, and Iapm in the in- to reveal progressively more closely connected subgraphs. The cores nermost core. Similarly, the task-negative network consists of Brod- are naturally nested, that is, V0 contains V1 which contains V2, and so mann regions 31, 30, 39, 32/10, 8, 20/21, and 35 which (with the ex- on, and, hence, we may think of the cores as constituting a hierarchy. ception of area 39) roughly map to PECg, PGm, SPL, PEm, PEc#1, TE, AITv, PIT, AITd, 35, ENT, PrS, TH, TF, 32, 10, 10o, FEF, 45, The innermost core Vkˆ is the top of this hierarchy. Define shells as follows: 8A, 8, 8B, and 31 in the innermost core. Sk = Vk \ Vk+1, 0 ≤ k ≤ k,ˆ In addition to these networks, the innermost core contains por- tions of prefrontal cortex (14, 13, 9, 12, 11, 14r, 13a, 13L, 13M, M9, where \ represents set difference operator. The shell Sk is simply 12l, 12m, 12o, 12r, 11l, 11m), cingulate cortex (25, 24, 23, 24a, 24b, those vertices that are in Vk but not in Vk+1. For k ≥ 0, let Ek ⊂ E 24c, 23c), thalamus (MD, Pul#1, MDmc, PL#3, Pul.o, PM#3, Cl#2, denote the set of edges between vertices in Vk. CM#2, Pcn, Li, VA, MDpc, VAmc, VLo, VPL), basal ganglia (SI#2, We now describe a formal algorithm for computing the cores and B#2, L#2, Cd, ABmg, Abpc, Bi, Bla, Lvl, Lv, Pu r, Ldi), temporal shells that yields deeper insight into the finer structure of each shell. lobe (Tpt, A1, TAa, ST1, ST2, ST3, TG, TPPro, 36, 36c, 36r), pari- The algorithm starts from (Vk,Ek) and yields (Vk+1,Ek+1) as well etal lobe (LIP, MIP), primary motor cortex (M1, M1-FL), and visual as a finer decomposition of Sk into a sequence of disjoint sub-shells cortex (V4). F ,F ,...,F a > b F k,1 k,2 k,mk . For , each element of the set k,a has All these vertices are shown in Figure S33. more edges to Vk+1 than each element of the set Fk,b.

Input: k, Vk, Ek Stability of the Innermost Core Given the structural and functional 1. Initially, set Vk+1 = Vk, Ek+1 = Ek. Set mk = 0. importance of the innermost core, we now show that it is stable with 2. while (some vertex in (Vk+1,Ek+1) has degree less than k + 1) respect to modest changes in the underlying network. (a) Set mk = mk + 1. We intuitively explain the basic notion of stability. Let a > b, v ∈ V and u ∈ V . Then, removing a connection between v and (b) Let F denote the set of all vertices in (V ,E ) that a b k,mk k+1 k+1 u can lead both vertices to move to outer cores. Conversely, adding have degree less than k + 1. a connection between v and u may lead for u to move to an inner (c) Vk+1 = Vk+1 \ Fk,mk . Let Ek+1 denote the set of edges core but cannot change the position of v. Thus, for vertices in the in- between vertices in Vk+1. nermost core, it is most interesting to study deletions of connections endwhile to other vertices in the innermost core, whereas for vertices outsides the innermost core (that is, in the crust), it most interesting to study additions of connections to vertices in the innermost core. Output: Vk+1, Ek+1, mk, {Fk,1,Fk,2,...,Fk,mk }, Sk = Vk \ mk Vk+1 = ∪n=1Fk,n. In Table S6, we enumerate all 383 vertices in decreasing order of the number of connections to the innermost core. We distinguish 122 members of the innermost core by color coding them. The first Applying the above algorithm to our network yields kˆ = 29. Fig- column shows number of connections to the innermost core. For ex- ure S34 shows that the core size decreases linearly with increasing k. ample, area 46 has 129 connections to the innermost core. For the 29 We enumerate all shells {Sk}k=0 and all finer sub-shells in Table S5. 122 members of the innermost core, the second column shows how Finally, using a technique similar to that in [27], we visually illustrate many connections can be safely deleted without removing the asso- the entire k-core decomposition in Figure S31. ciated vertex from the innermost core. For example, we can safely delete upto 100 connections between area 46 and the innermost core, Coreness Centrality. Coreness uncovers a sequence of progressively and it will still remain a member of the innermost core. The area more densely interconnected sub-networks. In the process, it implic- 24 has 111 connections to the innermost core and, so, we can delete itly defines a measure of topological centrality on the vertices. For 82 of these connections while still retaining it in the innermost core. example, for our network the innermost ring in Figure S31 is most As we go down the table, it can be seen that brain regions Pul#1, central and the outer most ring is least central. Table S5 can be in- SPL, PrS, and SMAr have exactly 29 connections to the innermost terpreted as listing the vertices in the ascending order of coreness core, and, hence, removing even a single connection from them to centrality, where all vertices within a fine shell are assigned the same the innermost core will remove them from the innermost core. Thus, coreness centrality value. The innermost fine shell F29,14 has the against random deletions of connections, we can say that area 46 is highest coreness centrality, and, once again, contains 8 brain regions more stable member of the innermost core, than area 24, which in in prefrontal cortex (32, 8B, 14, 10, 9, 11, 46, 12o) from a total of 11, turn is significantly more stable than Pul#1, SPL, PrS, and SMAr. thus corroborating Table 1 of the main text. A limitation of Table 1 For the remaining 261 vertices of the crust, the first column still is that it limits attention to top ten brain regions. Figure S31 can be shows number of connections to the innermost core, but the second used to overcome this limitation. For example, keeping vertex po- column now shows how many connections need to be added between sition identical to that in Figure S31, Figure S32 colors the vertices a vertex and the innermost core for the vertex to become a member according to betweenness centrality where hot colors represent high of the innermost core. The second column uses negative numbers – betweenness centrality and cool colors indicate low betweenness cen- since these connections have to be added. For example, any of the trality. It can be clearly seen that hot colors are concentrated in the brain regions V2, Pf#2, Ld#2, TFL, PGa, and VLc can be promoted inner rings. to the innermost core by simply adding one connection between itself and the innermost core. Task-Positive and Task-Negative Networks The task-positive net- In summary, modest changes in the database may move individ- work [28] consists of Brodmann regions 7, 7/40, 19, 6, 6/32, 46, ual affected brain regions up or down in the core hierarchy, but cannot 19/37, and Insula/frontal operculum which (with the exception of substantially change the global core structure.

5 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh 1. Kaiser M, Hilgetag CC (2006) Nonoptimal component placement, but short process- 18. Sherman SM, Guillery RW (2006) Exploring the thalamus and its role in cortical ing paths, due to long-distance projections in neural systems. PLoS Comput. Biol. function (The MIT Press, Cambridge, MA). 2:805-815. 19. Schmahmann JD, Pandya DN (2006) Fiber Pathways of the Brain (Oxford University 2. http://www.cocomac.org (2000). Press). 3. Stephan K, Zilles K, Kotter¨ R (2000) Coordinate-independent mapping of structural 20. Milgram S (1967) Small-world problem. Psychology Today 1:61-67. and functional data by objective relational transformation (ORT). Phil. Trans. R. 21. Watts DJ, Strogatz SH (1998) Collective dynamics of ’small-world’ networks. Nature Soc. Lond. B 355:37-54. 393:440-442. 4.K otter¨ R, Wanke E (2005) Mapping brains without coordinates. Phil. Trans. R. Soc. 22. Sporns O, Zwi J (2004) The small world of the cerebral cortex. Neuroinformatics Lond. B 360:751-766. 2:145-162. 5.K otter¨ R (2004) Online retrieval, processing, and visualization of primate connec- 23. Tononi G, Edelman GM (1998) Consciousness and complexity. Science 282:1846- tivity data from the CoCoMac database. Neuroinformatics 2:127-144. 1851. 6. Stephan KE, et al. (2001) Advanced database methodology for the collation of 24. Koch C, Laurent G (1999) Complexity and the nervous system. Science 284:96-98. connectivity data on the macaque brain (CoCoMac). Phil. Trans. R. Soc. Lond. B 25. Sherman SM, Guillery RW (1996) Functional organization of thalamocortical relays. 356:1159-1186. J Neurophysiol. 76:1367-1395. 7. Pandya DN, Seltzer B (1982) Intrinsic connections and architectonics of posterior 26. Weaver W (1948) Science and complexity. American Scientist 36:536-536. parietal cortex in the rhesus monkey. J. Comp. Neurol. 204:196-210. 27. Alvarez-Hamelin JI, Dall’Asta L, Barrat A, Vespignani A (2005) Large scale networks 8. Felleman DJ, Van Essen DC (1991) Distributed hierarchical processing in primate fingerprinting and visualization using the k-core decomposition. cerebral cortex. Cereb. Cortex 1:1-47. 28. Fox MD, et al. (2005) The human brain is intrinsically organized into dynamic, 9. Rockland KS, Drash GW (1996) Collateralized divergent feedback connections that anticorrelated functional networks. Proc Natl Acad Sci U S A 102:9673-9678. target multiple cortical areas. J. Comp. Neurol. 373:529-548. 29. Van Essen DC (2004) in The Visual Neurosciences, eds Chalupa L, Werner J (MIT 10. Paxinos G, Huang XF, Toga AW (1999) The Rhesus Monkey Brain in Stereotaxic Press), pp 507-521. Coordinates (Academic Press). 30. Orban GA, et al. (2003) Similarities and differences in motion processing between 11. Paxinos G, Huang XF, Petrides M, Toga AW (2008) The Rhesus Monkey Brain in the human and macaque brain: evidence from fMRI. Neuropsychologia 41:1757- Stereotaxic Coordinates, Second Edition (Academic Press). 1768. 12. Tollis IG, Di Battista G, Eades P, Tamassia R (1998) Graph Drawing: Algorithms for 31. Astafiev SV, et al. (2003) Functional organization of human intraparietal and frontal the Visualization of Graphs (Prentice Hall). cortex for attending, looking, and pointing. The Journal of Neuroscience 23:4689- 13. Lamping J, Rao R, Pirolli P (1995) A Focus+Context Technique Based on Hyperbolic 4699. Geometry for Visualizing Large Hierarchies (ACM/SIGCHI), pp 401–408. 32. Orban GA, Van Essen DC, Vanduffel W (2004) Comparative mapping of higher visual 14. Gonzalez RC, Woods RE (2008) Digital Image Processing (Addison-Wesley Pub areas in monkeys and humans. Trends in Cognitive Sciences 8:315-324. (Sd)), 3 edition. 15. Itten J (1961) The Art of Color (John Wiley & Sons, Inc, New York). 33. Orban GA, et al. (2006) Mapping the parietal cortex of human and non-human 16. Holten D (2006) Hierarchical edge bundles: Visualization of adjacency relations in primates. Neuropsychologia 44:2647-2667. hierarchical data. IEEE Trans. Vis. Comput. Graph. 12:741-748. 34. Vincent JL, et al. (2007) Intrinsic functional architecture in the anaesthetized mon- 17. Ungerleider LG, Mishkin M (1982) in Analysis of visual behavior, eds Ingle DJ, key brain. Nature 447:83-86. Goodale MA, Mansfield RJ (MIT Press, Cambridge, MA), pp 549-586.

6 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Fig. S1. Connectivity of the largest previous long distance network [1] within our visualization framework. The network consists of 95 vertices and 2,402 edges. By comparing this network to our network in Figure 1 of the main text, the richness of our data becomes apparent.

7 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh AP84-TE / BP82-46

PG91b-ITo SP89a-46 (a)

FV91-V1 / FV91-V4 / FV91-TF ^======RV99-TF / RV99-CA1 ======FV91-TH

BR98-THo BR98-CA1 (b)

Fig. S2. Connectivity between brain regions by different tracer injection studies. The notation x → y means that there is a connection from brain region x to y. By establishing an equivalence between AP84-TE and PG91b-IT and between BP82-46 and SP89a-46, the ﬁrst example can be used to infer that there is a reciprocal connection between inferotemporal area, which is often denoted as either TE or IT, and prefrontal area 46. Similarly, by establishing equivalences between regions with the same acronym (shown via dotted enclosing rectagles), the second example can be used to infer that there is a short circular path containing V1 and CA1 subﬁeld in the hippocampus, namely, V1 → V4 → TF → CA1 → TH → V1.

8 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh FL 14 25 FL 14 25 9 PFCd 9 PFCd FL 1 0 1 FL 0 1 1 PFCd 1 1 PFCd 0 1 14 0 1 0 14 0 0 1 9 1 1 9 0 0 25 1 0 1 25 00 0

I + (i) L+ I + (ii) L+ PCi IPL PF#1 7b PCi IPL PF#1 7b 24 LA#1 CCa 24 LA#1 CCa PCi 1 1 1 1 PCi 0 0 0 1 241 1 1 24 0 0 1 IPL 1 1 1 1 IPL 0 0 0 0 LA#1 1 1 1 LA#1 0 0 0 PF#1 1 1 1 1 PF#1 0 0 0 0 CCa 1 1 1 CCa 0 0 0 7b 1 1 1 1 7b 0 0 0 0

I + (iii) L+ IL+ (iv) + PMd F2 6D 6DR PMd F2 6D 6DR

F2 1 1 1 1 F2 0 1 0 1 PMd 11 1 1 PMd 0 0 0 1 6D 1 11 1 6D 0 0 0 0 6DR1 1 1 1 6DR 0 0 0 0

I + (v) L+ CCa 24 24d 24c’ CMAr 24c CCa 24 24d 24c’ CMAr 24c

CCa 1 1 1 11 1 CCa 0 0 0 0 1 1 24 1 1 1 1 1 1 24 0 0 0 0 0 0 24d 1 11 1 1 1 24d 0 0 0 0 0 0 24c’ 1 1 1 1 1 1 24c’ 0 0 0 0 0 0 CMAr 1 1 1 1 1 1 CMAr 0 0 00 0 0 24c 1 1 1 1 1 1 24c 0 0 0 0 1 0

I + (vi) L+

Fig. S3. Five examples of conflict between I and L relations. Sub-matrices of I+ and L+ corresponding to the conflict are shown for each case. In each matrix the entries in black are the original relations while entries in blue are the relations because of transitivity. Conflicts in each case are shown by underlining the relevant entry.

9 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh I+

J +

J L

L+

Fig. S4. The binary relations I and L are transitive, and let I+ and L+ denote the respective transitive closures. We define the conflict relation as the intersection between I+ and L+. We compute a subset J of I such that intersection of J+ and L+ is empty. This is a conflict-free identity relation, and can be safely used for merging.

10 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh DiE

FL#2

Pl#6 CgG#2 Ins

TL#2

OC#2 BG

0 50 100 150 200 250 300 350 nz = 276

Fig. S5. A matrix visualization of 143 remaining overlap relations in our hierarchical brain map. Rows and columns of the matrix correspond to the brain regions in Table S1 in the same order. The symbol “•” denotes the presence of an overlap relation between two corresponding brain regions. Given the symmetry of overlap relation, the lower and upper triangular parts are transposes of one another. For ease of visualization, we have divided the matrix into big container regions diencephalon (DiE), basal ganglia (BG), occipital lobe (OC#2), temporal lobe (TL#2), insula (Insula), cingulate cortex (CgG#2), parietal lobe (Pl#6), and frontal lobe (FL#2). Although, brain regions in FL#2 have overlap with brain regions CgG#2 and brain regions TL#2 has some overlap with brain regions in OC#2, Pl#6, and Insula, typically, overlap is limited to two brain regions within a container.

11 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh obe ral L po AL#4 ST1 em paAc

T CITd A1 TEm

CA1 TPOc

Tpt ST3 TAa

PaS L#1 MT STPg O Su#2 CITv PITd c DG MSTp c TPOi CL#4 ST2 i EO TH PGa p ProK V3d Sb i MTp t EI CA3 AITv a ECL TEa#3 PITv DLr l PrS MSTd ER#1 Pros. TPOr 36p IPa L paAlt V3v EC#2 Ts o Pa#2 FST VPP

ELr CIT b PIT 28m Hip AITd V3A DLc e TPO V6 TPg ELc V4t TPdgv S#1 STSf DI#1 TA 20 V1 A2 TPdgd MST V4v 36c 21 DP V3 Bla 36r EL STSd V6A V4d ProSt TFM STP#2 TPag TE OAa ABd a TPproD VOT l TFL ENT Abpc V2 u 35 PO#4 MB Iam V4 Bvl B s Iapm PHC STS Bi A a n TPPro STG I Iai ABvm s Pi#1 ABv TF a Idg OA I#2 CE#1 B#2 l Ial TG ABmg Ig#1 Ia#2 Ri#1 ME#1 AHA COp G e IPro t 29a-c VAC a 30 IA#1 36 PAC2 a 25 NLOT n l Ldi g u Insula Per#1 COa l CML 29d OC#2 Co g 23a i Ld#2 a n 29 Amyg PAC#1 Lvl i 23b TSA 26 Ldm Lv 23c TCv TL#2 SN C Sub.Th 23 L#2 SI#2 24a BG GPe 24d 24b CgG#2 24 Cd_t Cd_g 24c Cd PECg Pu_r 31 STR PCm Pu Pu_c PGm Cx Clau PCd#2 MB#2 PEc#1 OFC 5_Foot SPL Br Hyp PEm LD#1 AN AV MIP AM#1

e AIP PIP#1 PCip AD#1

b VIP Re LIP Pl#6 ML PAa PT#2 o LIPi LIPe C#4

L 7b 7#1 IPL Cim Clc PF#1 Cif

l GN

7a DiE

a Opt IL#2

t PFG#1 LGN MG Cdc

e i PG#1 Tha

PP Cl#2 CM#2

r Pcn Pf#2 a S2 PGop S1 FL#2 PN PFop belt_s MI#1

P 3#1 Cs#2 Csl PR#4 Pul#1 CMA#2 3a PI#3 PC#1 Ret Li SG SII-f 6#1 PM#3 PIm 3b M1 Pfc 1#1 6M PIp VN MD PL#3 PMm PIl-s 4a

2#1 8 PIc M1-HL FD#1 PLa#1 T

F3 VP#2 PIl

M1-FL MDl h

4b MDmc PLvm Pul.o 6D a

MI-body

M2-HL l

PFCorb PMl

F6 MDpc a FEF PLvl MI-of F2 6V VPL m

46 MDcd PLd MDfi

SMAc VL u

44 8A M2-FL s VA VPI MDpm MDdc 45 F7 14 6Vb OFO VPLc 9/46 F5 13

12 MDmf SMAr F4 10 VPS 9 VLo

11 VAdc VPLo 4c 8Ad ProM#2 14O 6b-beta 8B VLps X

9/46d 13M 6Va 10m VPM 10o VApc 46vr belt_sm 46d 45B M9 PrCO 11l OFap VLm

47/12

13L 8Ac 9/46v VLc 46f 10d 32 VAmc

46v

45A 12l

12m e 14r

b Gu

o 46dr 13a

10v

L PS

l D9

t 11m n 12r

12o o r F

Fig. S6. Hierarchical macaque brain map consisting of 383 regions in brain (Br) that is divided into cortex (Cx), diencephalon (DiE), and basal ganglia (BG). Further, cortex is divided into temporal lobe (TL#2), frontal lobe (FL#2), parietal lobe (Pl#6), occipital lobe (OC#2), insula (Insula), and cingulate cortex (CgG#2), and so on. Each brain region is represented via its acronym or abbreviation enclosed in a small colored rectangle. The acronyms are consistent with CoCoMac, which explains somewhat mechanical abbreviations such as CgG#2. The brain regions in the three outermost circles are leaves that cannot be further subdivided. Legend: We have used a color wheel for better discrimination amongst brain regions. For the leaf brain regions in the two outermost circles, we have rotated the color wheel by 120 degrees and 240 degrees. Table S1 enumerates the entire hierarchical brain map and provides a complete index to acronyms of the brain regions, and has been color coded for wider accessibility. See Figures S7-S14 that zoom into the hierarchical brain map and Figure S15 that uses an alternative color scheme.

12 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Insula OC#2

TL#2

BG CgG#2

Pl#6

DiE

FL#2

Fig. S7. Hierarchical decomposition of brain (Br) into cortex (Cx), diencephalon (DiE), and basal ganglia (BG), and cortex into temporal lobe (TL#2), frontal lobe (FL#2), parietal lobe (Pl#6), occipital lobe (OC#2), insula (Insula), and cingulate cortex (CgG#2). The descendants of DiE, BG, TL#2, FL#2, Pl#6, OC#2, Insula, and CgG#2 are not shown here, but are shown in subsequent ﬁgures.

13 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh AL#4 ST1

paAc

CITd A1 TEm

CA1 TPOc

Tpt ST3 TAa

PaS L#1

STPg MT Su#2 CITv

PITd DG TPOi MSTp CL#4 ST2 TH EO PGa ProK Sb MTp EI CA3 AITv ECL TEa#3 PITv PrS MSTd ER#1 Pros. TPOr 36p IPa paAlt Ts EC#2 Pa#2 FST

ELr CIT PIT 28m Hip AITd

TPO TPg ELc TPdgv S#1 STSf

TA 20 TPdgd A2 MST 36c 21

36r EL STSd

TFM STP#2 TPag TPproD TE OAa TFL ENT 35 PHC STS

TPPro STG

Per#1

TCv TL#2

Fig. S8. Hierarchical decomposition of temporal lobe (TL#2).

14 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh V3d

DLr

V3v VPP

V3A DLc V6 V4t DI#1 V1 V4v V3 DP V6A V4d ProSt VOT V2 V4 PO#4

VAC

OC#2

Fig. S9. Hierarchical decomposition of occipital lobe (OC#2).

15 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Bla

ABd Abpc MB Bvl Bi A ABv ABvm I#2 CE#1 B#2 ABmg ME#1 AHA COp

PAC2 NLOT Ldi COa Co Ld#2 Amyg PAC#1 Lvl Ldm Lv SN Sub.Th L#2 SI#2 BG GPe Cd_t Cd_g Cd Pu_r STR Pu Pu_c Clau

Fig. S10. Hierarchical decomposition of basal ganglia (BG).

16 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Hyp LD#1 AN AV AM#1 AD#1 Re ML PAa PT#2 C#4 Clc Cif Cim GN DiE IL#2 LGN MG Cdc

Tha Cl#2 CM#2 Pcn Pf#2 PN MI#1 Cs#2 Csl Pul#1 PI#3 Ret Li SG PM#3 PIm PIp VN MD PL#3 PMm PIl-s

PLa#1 PIc VP#2 MDl PIl MDmc PLvm Pul.o PMl MDpc PLvl VPL MDcd PLd MDfi VL

VA VPI MDpm MDdc

VPLc VPS MDmf VLo VAdc VPLo

VLps X

VApc VPM

VLm

VLc

VAmc

Fig. S11. Hierarchical decomposition of diencephalon (DiE).

17 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh FL#2

6#1 Pfc M1 6M

4a 8

M1-HL FD#1 F3 4b M1-FL 6D MI-body M2-HL PFCorb F6 FEF MI-of F2 6V 46 SMAc 44 M2-FL 8A 45

F7 6Vb OFO 14 9/46 F5 13 SMAr F4 12 10 9

11 4c 8Ad ProM#2 14O 6b-beta 8B

9/46d 13M 6Va 10m 46vr 10o belt_sm 46d 45B M9 11l PrCO OFap

47/12

13L 8Ac 9/46v 46f 10d 32

46v L9

45A 12l

12m 14r

Gu 46dr 13a PS 10v

11m 12r

12o

Fig. S12. Hierarchical decomposition of frontal lobe (FL#2).

18 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh PECg 31 PCm PGm PEc#1 PCd#2 5_Foot SPL PEm MIP AIP PIP#1 PCip VIP LIP Pl#6 LIPi LIPe 7b IPL 7#1 PF#1 7a PFG#1 Opt PG#1 PP PGop S2 PFop belt_s S1 3#1 PR#4 CMA#2 3a PC#1 SII-f 3b 1#1

2#1

Fig. S13. Hierarchical decomposition of parietal lobe (Pl#6).

19 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Iam Iapm Iai Pi#1 Idg Ial Ig#1 Ri#1 Ia#2 IPro 29a-c 30 IA#1 25

Insula 23a CML 29d 29 26 23c 23b TSA 23 24a 24d 24b CgG#2 24 24c

Fig. S14. Hierarchical decomposition of insula (Insula) and cingulate cortex (CgG#2).

20 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh obe ral L po AL#4 ST1 em paAc

T CITd A1 TEm

CA1 TPOc

Tpt ST3 TAa

PaS L#1 MT STPg O Su#2 CITv PITd c DG MSTp c TPOi CL#4 ST2 i EO TH PGa p ProK V3d Sb i MTp t EI CA3 AITv a ECL TEa#3 PITv DLr l PrS MSTd ER#1 Pros. TPOr 36p IPa L paAlt V3v EC#2 Ts o Pa#2 FST VPP

e AIP PIP#1 PCip AD#1

b VIP Re LIP Pl#6 ML PAa PT#2 o LIPi LIPe C#4

L 7b 7#1 IPL Cim Clc PF#1 Cif

l GN

7a DiE

a Opt IL#2

t PFG#1 LGN MG Cdc

e i PG#1 Tha

PP Cl#2 CM#2

r Pcn Pf#2 a S2 PGop S1 FL#2 PN PFop belt_s MI#1

P 3#1 Cs#2 Csl PR#4 Pul#1 CMA#2 3a PI#3 PC#1 Ret Li SG SII-f 6#1 PM#3 PIm 3b M1 Pfc 1#1 6M PIp VN MD PL#3 PMm PIl-s 4a

2#1 8 PIc M1-HL FD#1 PLa#1 T

F3 VP#2 PIl

M1-FL MDl h

4b MDmc PLvm Pul.o 6D a

MI-body

M2-HL l

PFCorb PMl

F6 MDpc a FEF PLvl MI-of F2 6V VPL m

46 MDcd PLd MDfi

SMAc VL u

44 8A M2-FL s VA VPI MDpm MDdc 45 F7 14 6Vb OFO VPLc 9/46 F5 13

12 MDmf SMAr F4 10 VPS 9 VLo

11 VAdc VPLo 4c 8Ad ProM#2 14O 6b-beta 8B VLps X

9/46d 13M 6Va 10m VPM 10o VApc 46vr belt_sm 46d 45B M9 PrCO 11l OFap VLm

47/12

13L 8Ac 9/46v VLc 46f 10d 32 VAmc

46v

45A 12l

12m e 14r

b Gu

o 46dr 13a

10v

L PS

l D9

t 11m n 12r

12o o r F

Fig. S15. An alternative visualization where the text labels have been drawn in black on light background, and in white on dark background, in order to improve the accessibility of the ﬁgure.

21 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Bla Bla

ABd ABd Abpc Abpc MB MB Bvl Bvl Bi Bi A A ABv ABvm ABv ABvm I#2 CE#1 I#2 CE#1 B#2 ABmg B#2 ABmg ME#1 AHA COp ME#1 AHA COp

PAC2 NLOT PAC2 NLOT Ldi Ldi COa COa Co Co Ld#2 Ld#2 Amyg PAC#1 Lvl Amyg PAC#1 Lvl Ldm Lv Ldm Lv SN SN Sub.Th Sub.Th L#2 SI#2 L#2 SI#2 BG GPe BG GPe Cd_t Cd_g Cd_t Cd_g Cd Cd Pu_r Pu_r STR STR Pu Pu_c Pu Pu_c Clau Clau MB#2 MB#2 OFC OFC Br Hyp Br Hyp LD#1 LD#1 AN AV AN AV AM#1 AM#1 AD#1 AD#1 Re Re ML PAa PT#2 ML PAa PT#2 C#4 C#4 Clc Clc Cif Cim Cif Cim GN GN DiE DiE IL#2 LGN MG Cdc IL#2 LGN MG Cdc

Tha Cl#2 CM#2 Tha Cl#2 CM#2 Pcn Pf#2 Pcn Pf#2 PN PN MI#1 MI#1 Cs#2 Csl Cs#2 Csl Pul#1 Pul#1 PI#3 Ret PI#3 Ret Li SG Li SG PM#3 PIm PM#3 PIm PIp PIp MD PL#3 PMm PIl-s MD PL#3 PMm PIl-s

PLa#1 PIc PLa#1 PIc MDl PIl MDl PIl MDmc PLvm Pul.o MDmc PLvm Pul.o PMl PMl MDpc PLvl MDpc PLvl

MDcd PLd MDcd PLd MDfi MDfi

MDpm MDdc MDpm MDdc

MDmf MDmf (a) (b)

Bla Bla

ABd ABd Abpc Abpc MB MB Bvl Bvl Bi Bi A A ABvm ABv ABv ABvm I#2 CE#1 B#2 I#2 CE#1 ABmg B#2 ABmg AHA ME#1 COp ME#1 AHA COp PAC2 NLOT PAC2 NLOT Ldi Ldi COa Co COa Ld#2 Co PAC#1 Ld#2 Amyg Lvl Amyg PAC#1 Lvl Ldm Lv Ldm Lv SN SN L#2 Sub.Th Sub.Th SI#2 L#2 SI#2 BG GPe BG GPe Cd_t Cd_g Cd_t Cd_g Cd Cd Pu_r Pu_r STR Pu STR Pu_c Pu Pu_c Clau Clau MB#2 MB#2 Br OFC OFC Hyp Br Hyp LD#1 LD#1 AN AV AN AV AM#1 AM#1 AD#1 AD#1 ML PT#2 Re Re PAa ML PAa PT#2 C#4 C#4 Cim Clc Clc Cif Cif Cim GN DiE GN IL#2 Cdc DiE LGN MG IL#2 LGN MG Cdc Tha Cl#2 CM#2 Tha Pcn Cl#2 CM#2 Pf#2 Pcn Pf#2 PN MI#1 PN Cs#2 MI#1 Csl Cs#2 Csl Pul#1 PI#3 Pul#1 Ret PI#3 Ret Li PM#3 SG Li SG PIm PM#3 PIm PIp PIp MD PMm PIl-s PL#3 MD PL#3 PMm PIl-s PIc PLa#1 PLa#1 PIc PIl MDl MDl PIl MDmc Pul.o PLvm MDmc PLvm Pul.o MDpc PMl PMl PLvl MDpc PLvl MDcd PLd MDfi MDcd PLd MDfi

MDpm MDdc MDpm MDdc

MDmf MDmf (c) (b)

Fig. S16. Example to show visualization of network edges, and effect of bundling. Areas Bla and MB are in amygdala, and areas MD and MDmc are in thalamus. Three long distance connections, from Bla to MDmc, MB to MDmc, and MB to MD, are shown. The control polygon of the connection between Bla and MDmc is through nodes, Bla, B#2, Amyg, BG, Br, Die, Tha, MD, and MDmc. It is easy to observe that the control polygon for the connection between MB and MDmc is very similar, in-fact it differs only in the last control point, MB instead of Bla, and similarly for the connection between MB and MD. Thus tracing from the areas in amygdala, splines of all three connections would bundle together left of the least common control point, B#2, rise up to the least common ancestor, Br, and then come down to Tha, where just above MD, the splines would split, and end at their respective destinations, MD and MDmc. The amount of bundling is controlled by the bundling factor β. Four different value of the bundling factor β are shown. (a) β = 0; (a) β = 0.5; (a) β = 0.8; and (a) β = 0.993. It can be seen that as bundling factor increases, more clarity ensues.

22 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh (a) (b)

Fig. S17. Long distance network in the macaque brain consisting of 383 hierarchically organized brain regions and 6,602 directed connections shown with four different value of the bundling factor β. (a) β = 0; (a) β = 0.8; (a) β = 0.95; and (a) β = 0.993. It can be seen that as bundling factor increases, more clarity ensues. For all other ﬁgures in this paper, the bundling factor has been chosen to be 0.993.

23 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh (a) (b)

(c) (d) Fig. S18. To demonstrate comprehensiveness, the figure illustrates that sub-networks corresponding to four classical fiber systems are all contained within our network. (a) The fiber system of [8] illustrating connectivity of visual cortex with temporal lobe, parietal lobe, and frontal lobe. (b) The fiber system of [17] illustrating the dorsal (“where”) pathway from occipital lobe to parietal lobe and the ventral (“what”) pathway from occipital lobe to temporal lobe. (c) Superior longitudinal fasciculus [19] between parietal and frontal lobes that mediates the initiation of motor activity as well as visual awareness/attention. (d) Thalamocor- tical Relays [18] illustrating the extensive coupling between cortex and thalamus. To further emphasize the richness of our network, Figures S19, S20, and S21 illustrate sub-networks corresponding to other classical fiber systems described in [19], namely, arcuate fasciculus, cingulum bundle, extreme capsule, fronto- occipital fasciculus, inferior longitudinal fasciculus, middle longitudinal fasciculus, uncinate fasciculus, connectivity between cortex and striatum/claustrum, connectivity between amygdala and cortex, and connectivity between amygdala and diencephalon.

24 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh obe obe ral L ral L mpo mpo Te Te

TPOc Tpt O O cc cc ip EO TH ip it it a EI a l ECL l PrS TPOr ER#1 L 36p L o EC#2 o b ELr b e 28m e

TPO TPg ELc

TPdgd 36c

36r EL TFM TPag a a TPproD l l TFL ENT u B u 35 B s s a a n n TPPro I s I s a TF a l l TG G G e e t a t 29a-c a 30 36 a n a 25 n l l g g u u l 29d l g i g i a a n n 29 i i

C C

e e

b b

o o

L L l

l 7a

a Opt

t t

e e

i PG#1

r r

a a

P P

T F3 h h

a a 6D

l l

a a F6

m F2 m F2

u SMAc

s s

F7 F7 14 SMAr

11 8Ad 8Ad

14O

9/46d 9/46d

46d

11l

e e 14r

b b

o o

L L

l D9

a a

t 11m n n

o o r r F F (a) (b)

obe obe ral L ral L mpo AL#4 mpo Te Te

TPOc

ST3 TAa L#1 O O cc cc TPOi CL#4 ST2 TH ip ip ita ita l l TPOr 36p IPa L L paAlt o o b b e e TPO V6 TPg TPdgv TPdgd 36c DP 36r V6A TPag TPproD la la u B u PO#4 B s Iam s Iapm a a n TPPro n I Iai s I s Pi#1 a a Idg l l Ial TG Ig#1 Ia#2 Ri#1 G G e e t a t a 36 a n a n l l g g u u Insula l l g i g i a a n n i i

C C

24b 24a 24 24c

PGm

e e

b b

o o

L L l

l 7a

a Opt

t t

e e

i PG#1

r r

a a

P P

T T

h h

a a 6D

l l

a a

m m F2

u u

s 45 s F7

8Ad 8Ad

8B 9/46d

46d 45B M9

47/12

45A

e e

b b

o o

L L

l l D9

a a

t t

n n

o o r r F F (c) (d)

Fig. S19. Sub-networks corresponding to various classical ﬁber systems in the brain [19]: (a) AF: Arcuate Fasciculus; (b) CB: Cingulum Bundle; (c) EmC: Extreme Capsule; (d) FOF: Fronto-Occipital Fasciculus.

25 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh obe obe ral L ral L po po AL#4 em em paAc

T CITd T A1

TPOc

Tpt TAa

L#1 MT O O

CITv PITd c c MSTp c c TPOi i CL#4 i TH p PGa p V3d it ProK it AITv a a TEa#3 PITv DLr l l MSTd TPOr 36p IPa L IPa L V3v o paAlt o FST Pa#2

CIT b b PIT DLc e e

TPO TPg V4t

20 V1 MST V4v 36c V3 DP DP 36r TFM V4d TPag TPproD la TFL la TFL u V2 u V4 B B s s a a n TPPro n I s I s TF a TF a l l TG G G e e t a t a 36 30 a n a n l l g g u u l l g i g 23a i a a n n i i 23c 23b TSA C C

e e b

b LIP o

o LIPi LIPe

L L l

l 7a

a Opt Opt

t t

e e

i PG#1

r r

a a

P P

T T

h h

a a

l l

a a

m m

u u

s s

e e

b b

o o

L L

l l

a a

t t

n n

o o r r F F (a) (b)

obe obe ral L ral L mpo ST1 mpo Te Te

O MT O cc cc EO TH ip TH ip it it EI AITv a a ECL TEa#3 l l ER#1 36p IPa L L V3v EC#2 o EC#2 FST o ELr b b 28m e 28m PIT e V6 TPg ELc TPdgv TA V1 TPdgd MST 36c Bla V3 36r EL TFM V4d TPag TE a TPproD ABd a l TFL ENT Abpc l ENT V2 u 35 MB u 35 Bvl B Iam V4 B s Bi s Iapm STS A a a n TPPro n STG I s I Iai s ABv ABvm TF a TF a I#2 CE#1 OA B#2 l l TG ABmg Ial TG ME#1 AHA COp G G e e t a t a 36 PAC2 a 25 NLOT n a 25 n l l Ldi g g u COa u Insula Per#1 Co l l g i g i Ld#2 a a n Amyg PAC#1 Lvl n i Lv i

C C L#2 23 24b 24a 24b 24 24 Cd_t Cd_g 24c 24c Cd PECg Pu_r Pu Pu_c PGm Clau PEc#1 SPL PEm

MIP

e e b

b LIP

o o L

L IPL 7#1

PF#1

l l

a a

t t PFG#1

e e

i PG#1

r r a

a PFop

P P

T T FD#1

h h

a a 6D

l l

a a FEF

m 46

u u

s s 45 14 F7 6Vb 14

13 13

10 12 10

11 11

14O

13M 13M 10m 6Va 10m

10o 10o

11l PrCO 11l

47/12

13L 13L

10d 32 32

12l

12m

e e 14r 14r

b b

o 13a 13a

10v

L L

l l

a a

t 11m 11m n n 12r

12o o o r r F F (c) (d)

Fig. S20. Sub-networks corresponding to various classical ﬁber systems in the brain [19]: (a) ILF: Inferior Longitudinal Fasciculus; (b) MdLf: Middle Longitudinal Fasciculus; (c) UF: Uncinate Fasciculus, (d) cortex and striatum/claustrum.

26 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh obe obe ral L ral L mpo mpo Te Te

CA1

MT O O cc cc TH ip ip it it EI CA3 AITv a a TEa#3 l l Pros. L L 36p o o

ELr CIT b b PIT 28m Hip AITd e e

ELc S#1 TA 20 V1 MST

36c 21 Bla Bla 36r EL STSd

a TE ABd a l ENT Abpc l Abpc V2 u 35 MB u MB Iam V4 Bvl B B s Iapm PHC Bi s A a A a n TPPro STG n I Iai ABvm s I s Pi#1 ABv TF a a Idg I#2 CE#1 CE#1 B#2 l B#2 l TG ABmg ABmg Ig#1 Ia#2 ME#1 AHA COp G ME#1 AHA COp G e e t a t a 36 PAC2 a 25 NLOT n a n l l Ldi g Ldi g u Insula COa u COa Per#1 Co l l g i g i Ld#2 a a n Amyg PAC#1 Lvl n Amyg PAC#1 i Lv i Lv C L#2 C L#2

Hyp LD#1

AM#1

e e b

b Re

ML PAa PT#2

o o

L L

Cif Cim

l l

a a

t t Cdc

e e

i i

r r

a a

P P

CMA#2 Pul#1 Li 6#1 PM#3

T FD#1 T

h MDmc a a

l l

a a

46 m

MDfi u u

s s MDpm 45 14

12 10

46v

12l

e e 14r

b Gu

o 13a

L L

l l

a a

t 11m n

n 12o o o r r F F (a) (b)

Fig. S21. Sub-networks corresponding to various classical ﬁber systems in the brain: (a) amygdala and cortex, (b) amygdala and diencephalon.

27 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh 1

0.9

0.8

0.7 x) ≥

0.6

0.5

0.4

0.3 Probability(degree

0.2

0.1

0 0 50 100 150 x

Fig. S22. The linear-linear plot shows the empirical complementary cumulative degree distribution (circles) and the complementary cumulative distribution of the maximum entropy exponential distribution ﬁt (dashed line), λ−1 exp(−x/λ), λ = 27.2, over the entire range of data.

28 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh obe ral L po AL#4 ST1 em paAc

T CITd A1 TEm

CA1 TPOc

Tpt ST3 TAa

PaS L#1 MT STPg O Su#2 CITv PITd c DG MSTp c TPOi CL#4 ST2 i EO TH PGa p ProK V3d Sb i MTp t EI CA3 AITv a ECL TEa#3 PITv DLr l PrS MSTd ER#1 Pros. TPOr 36p IPa L paAlt V3v EC#2 Ts o Pa#2 FST VPP

e AIP PIP#1 PCip AD#1

b VIP Re LIP Pl#6 ML PAa PT#2 o LIPi LIPe C#4

L 7b 7#1 IPL Cim Clc PF#1 Cif

l GN

7a DiE

a Opt IL#2

t PFG#1 LGN MG Cdc

e i PG#1 Tha

PP Cl#2 CM#2

r Pcn Pf#2 a S2 PGop S1 FL#2 PN PFop belt_s MI#1

P 3#1 Cs#2 Csl PR#4 Pul#1 CMA#2 3a PI#3 PC#1 Ret Li SG SII-f 6#1 PM#3 PIm 3b M1 Pfc 1#1 6M PIp VN MD PL#3 PMm PIl-s 4a

2#1 8 PIc M1-HL FD#1 PLa#1 T

F3 VP#2 PIl

M1-FL MDl h

4b MDmc PLvm Pul.o 6D a

MI-body

M2-HL l

PFCorb PMl

F6 MDpc a FEF PLvl MI-of F2 6V VPL m

46 MDcd PLd MDfi

SMAc VL u

44 8A M2-FL s VA VPI MDpm MDdc 45 F7 14 6Vb OFO VPLc 9/46 F5 13

12 MDmf SMAr F4 10 VPS 9 VLo

11 VAdc VPLo 4c 8Ad ProM#2 14O 6b-beta 8B VLps X

9/46d 13M 6Va 10m VPM 10o VApc 46vr belt_sm 46d 45B M9 PrCO 11l OFap VLm

47/12

13L 8Ac 9/46v VLc 46f 10d 32 VAmc

46v

45A 12l

12m e 14r

b Gu

o 46dr 13a

10v

L PS

l D9

t 11m n 12r

12o o r F

1 2 4 7 12 22 40 73 114

Fig. S23. The color of each vertex is a measure of how often the brain region corresponding to the vertex, and all brain regions merged into it (as reported in Table S1), have been studied in the literature reports compiled by CoCoMac. The (“hot”) dark red vertices are those that have been studied the maximum number of times, while (“cool”) dark blue vertices are those that have been studied the minimum number of times. The color bar is shown in the bottom right.

29 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh obe ral L po AL#4 ST1 em paAc

T CITd A1 TEm

CA1 TPOc

Tpt ST3 TAa

PaS L#1 MT STPg O Su#2 CITv PITd c DG MSTp c TPOi CL#4 ST2 i EO TH PGa p ProK V3d Sb i MTp t EI CA3 AITv a ECL TEa#3 PITv DLr l PrS MSTd ER#1 Pros. TPOr 36p IPa L paAlt V3v EC#2 Ts o Pa#2 FST VPP

e AIP PIP#1 PCip AD#1

b VIP Re LIP Pl#6 ML PAa PT#2 o LIPi LIPe C#4

L 7b 7#1 IPL Cim Clc PF#1 Cif

l GN

7a DiE

a Opt IL#2

t PFG#1 LGN MG Cdc

e i PG#1 Tha

PP Cl#2 CM#2

r Pcn Pf#2 a S2 PGop S1 FL#2 PN PFop belt_s MI#1

P 3#1 Cs#2 Csl PR#4 Pul#1 CMA#2 3a PI#3 PC#1 Ret Li SG SII-f 6#1 PM#3 PIm 3b M1 Pfc 1#1 6M PIp VN MD PL#3 PMm PIl-s 4a

2#1 8 PIc M1-HL FD#1 PLa#1 T

F3 VP#2 PIl

M1-FL MDl h

4b MDmc PLvm Pul.o 6D a

MI-body

M2-HL l

PFCorb PMl

F6 MDpc a FEF PLvl MI-of F2 6V VPL m

46 MDcd PLd MDfi

SMAc VL u

44 8A M2-FL s VA VPI MDpm MDdc 45 F7 14 6Vb OFO VPLc 9/46 F5 13

12 MDmf SMAr F4 10 VPS 9 VLo

11 VAdc VPLo 4c 8Ad ProM#2 14O 6b-beta 8B VLps X

9/46d 13M 6Va 10m VPM 10o VApc 46vr belt_sm 46d 45B M9 PrCO 11l OFap VLm

47/12

13L 8Ac 9/46v VLc 46f 10d 32 VAmc

46v

45A 12l

12m e 14r

b Gu

o 46dr 13a

10v

L PS

l D9

t 11m n 12r

12o o r F

0 1 4 9 21 44 94 199 349

Fig. S24. The color of each vertex is a measure of how many connections are reported for the brain region corresponding to the vertex, and all brain regions that merged into it (as reported in Table S1), in the literature reports compiled by CoCoMac. Note that some connections may be reported multiple times by different literature reports. Each such duplicate connection is counted. The (“hot”) dark red vertices are those that have the maximum number of connections, while (“cool”) dark blue color vertices are those that have the minimum number of connections. The color bar is shown in the bottom right.

30 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh obe ral L po AL#4 ST1 em paAc

T CITd A1 TEm

CA1 TPOc

Tpt ST3 TAa

PaS L#1 MT STPg O Su#2 CITv PITd c DG MSTp c TPOi CL#4 ST2 i EO TH PGa p ProK V3d Sb i MTp t EI CA3 AITv a ECL TEa#3 PITv DLr l PrS MSTd ER#1 Pros. TPOr 36p IPa L paAlt V3v EC#2 Ts o Pa#2 FST VPP

e AIP PIP#1 PCip AD#1

b VIP Re LIP Pl#6 ML PAa PT#2 o LIPi LIPe C#4

L 7b 7#1 IPL Cim Clc PF#1 Cif

l GN

7a DiE

a Opt IL#2

t PFG#1 LGN MG Cdc

e i PG#1 Tha

PP Cl#2 CM#2

r Pcn Pf#2 a S2 PGop S1 FL#2 PN PFop belt_s MI#1

P 3#1 Cs#2 Csl PR#4 Pul#1 CMA#2 3a PI#3 PC#1 Ret Li SG SII-f 6#1 PM#3 PIm 3b M1 Pfc 1#1 6M PIp VN MD PL#3 PMm PIl-s 4a

2#1 8 PIc M1-HL FD#1 PLa#1 T

F3 VP#2 PIl

M1-FL MDl h

4b MDmc PLvm Pul.o 6D a

MI-body

M2-HL l

PFCorb PMl

F6 MDpc a FEF PLvl MI-of F2 6V VPL m

46 MDcd PLd MDfi

SMAc VL u

44 8A M2-FL s VA VPI MDpm MDdc 45 F7 14 6Vb OFO VPLc 9/46 F5 13

12 MDmf SMAr F4 10 VPS 9 VLo

11 VAdc VPLo 4c 8Ad ProM#2 14O 6b-beta 8B VLps X

9/46d 13M 6Va 10m VPM 10o VApc 46vr belt_sm 46d 45B M9 PrCO 11l OFap VLm

47/12

13L 8Ac 9/46v VLc 46f 10d 32 VAmc

46v

45A 12l

12m e 14r

b Gu

o 46dr 13a

10v

L PS

l D9

t 11m n 12r

12o o r F

0 1 3 7 15 30 59 117 194

Fig. S25. The color of each vertex is a measure of its degree in the ﬁnal network. The (“hot”) dark red vertices are those that have the highest degree, while (“cool”) dark blue vertices are those that have the lowest degree. The color bar is shown in the bottom right.

31 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh 2 10

1 10 brain region in CoCoMac Number of connections reported for a

0 10 0 1 2 10 10 10 Number of times a brain region is studied in CoCoMac

Fig. S26. A plot of the number of times a brain region is studied, against its number of connections as reported in CoCoMac. For each brain region not only the region itself, but all regions that merge into it (as reported in Table S1), are accounted for. The red crosses correspond to brain regions in prefrontal cortex.

32 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh 2 10

1 10 Degree of a brain region in our network

0 10 0 1 2 10 10 10 Number of times a brain region is studied in CoCoMac

Fig. S27. A plot of the number of times a brain region is studied in CoCoMac, against its degree in the ﬁnal network. For each brain region not only the region itself, but all regions that merge into it (as reported in Table S1), are accounted for. The red crosses correspond to brain regions in prefrontal cortex.

33 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh 2 10

1 10 Degree of a brain region in our network

0 10 0 1 2 10 10 10 Number of connections reported for a brain region in CoCoMac

Fig. S28. A plot of the number of connections of a brain region reported in CoCoMac, against its degree in the ﬁnal network. For each brain region not only the region itself, but all regions that merge into it (as reported in Table S1), are accounted for. The red crosses correspond to brain regions in prefrontal cortex.

34 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh 4 10

3 10

2 10

1 10

0 10 Betweeness Centrality of a brain region in our network

−1 10

0 1 2 10 10 10 Degree of a brain region in our network

Fig. S29. A plot of the degree of a brain region in the ﬁnal network, against its betweenness centrality. The red crosses correspond to brain regions in prefrontal cortex.

35 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Fig. S30. The innermost core for the undirected version of our network. The innermost core is a central sub-network that is far more tightly integrated than the overall network, information likely spreads more swiftly within the innermost core than through the overall network, the overall network communicates with itself mainly through the innermost core, and the innermost core contains major components of the task-positive and task-negative networks derived via functional imaging research [28].

36 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Lobe oral mp Te

O cc TPOi ip Sb CITd it Su#2 Pa#2 a DLr l DG MTp 21 DLc L CA3 o PHC b TEm V3d VPP e

PITd DI#1 V4v

20 ELc PITv ProK 28m OAa

AL#4 TPdgd Hip EO PaS

STG TA 36p CL#4 STPg VOT ProSt TPdgv paAc

CIT

ECL MSTp

Pros. paAlt TPproD S#1 V4d L#1 Per#1 ELr CITv MST a STSd l TEa#3 ER#1 A2 CA1 u EL TPOr B TPag V4t s PGa IPa V3A a n PrS MT V3 EC#2 s I FST V3v OA a IPro MSTd ABd TPg I#2 l EI Bvl PO#4 V6 G A1 V6A ABv DP V1 ST1 a ABvm TAa ST2 Tpt n TFL ST3 Ial A e V4 V2 Amyg COp g t 26 TFM NLOT l CML TPOc AHA Co a AITv i l MB ME#1 a Ri#1 36c u Insula TPPro CE#1 29d 30 AITd PAC2

g STS 29 PIT COa n Pi#1 Ia#2 Iapm TPO Abpc Bi i 29a-c TH PAC#1 Bla SN ENT TE Sub.Th C 36r 23a Iam TG TSA 35 36 ABmg B#2 GPe 23b Ig#1 Iai Ldi Ld#2 Cd_t TF Lv Idg 25 Cd_g SI#2 L#2 Lvl 24d 24a 23c 23 Pu_c Pu PECg Cd 24b24c MB#2 SPL PEc#1 31 24 Clau Pu_r OFC 5_Foot PGm MIP PEm Hyp AV LD#1 AIP PIP#1 VIP IPL LIP AM#1 7b Pcn AN 7#1 Re AD#1 7a PAa LIPi PFG#1 PF#1 PG#1 MD Cl#2

e S2 6M CM#2 Clc PT#2

PM#3 Pf#2 b LIPe Li M1 F7 8B 14 ML

32 o Opt 46 10 9 Cdc

11 MG

13a L 6D 13 12o Csl F6 M1-FL Cif Cim C#4 8A 6V 12l 12 MDpc 45

l 2#1 F3 F2 PGop F5 PS 14r

3a VAmc SG a MDmc

6#1 t LGN 46v 13L

10o

PR#4 S1 11m

e VPL Pul#1 i PL#3 Ret IL#2

3#1 12m r PP PFop 1#1 VA 3b M9 Pul.o 13M 8 11l

a belt_s PI#3

FEF 12r P Cs#2 M1-HL SMAr MI#1 46d F4 PrCO CMA#2 MI-of VLo SII-f PC#1 X MI-body MDdc PN PIl PIm VPLc

VLc PIl-s PIc 6Va MDfi PIp

PMm VLm MDmf T

8Ad PMl 6Vb h VPM

4a 45A FD#1

VPLo Tha a

VLps

9/46d VApc PLd l

M2-FL D9 a

4b 4c ProM#2 belt_sm PLa#1 m PLvl

VL MDpm M2-HL 10m

PLvm u Gu VPI MDcd s

47/12 MDl SMAc

44 VPS 45B

6b-beta 9/46v VN

PFCorb 8Ac VAdc

OFap VP#2

14O

10v

46dr 46vr

OFO

10d

e 46f

n o r F

Fig. S31. Starting from the center, the innermost 14 rings correspond to the ﬁne shells of the innermost core. The ﬁnest shell F29,14 is at the center, followed by F29,13, and so on, until F29,1. The next 28 rings correspond to the shells S28,S27,...,S1, in that order from center to the periphery. The angular position of each vertex within a ring is the same its angular position in Figure S6. The color of each vertex is the same as its color in Figure S6.

37 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Lobe oral mp Te

O cc TPOi ip Sb CITd it Su#2 Pa#2 a DLr l DG MTp 21 DLc L CA3 o PHC b TEm V3d VPP e

PITd DI#1 V4v

20 ELc PITv ProK 28m OAa

AL#4 TPdgd Hip EO PaS

STG TA 36p CL#4 STPg VOT ProSt TPdgv paAc

CIT

ECL MSTp

e S2 6M CM#2 Clc PT#2

PM#3 Pf#2 b LIPe Li M1 F7 8B 14 ML

32 o Opt 46 10 9 Cdc

11 MG

13a L 6D 13 12o Csl F6 M1-FL Cif Cim C#4 8A 6V 12l 12 MDpc 45

l 2#1 F3 F2 PGop F5 PS 14r

3a VAmc SG a MDmc

6#1 t LGN 46v 13L

10o

PR#4 S1 11m

e VPL Pul#1 i PL#3 Ret IL#2

3#1 12m r PP PFop 1#1 VA 3b M9 Pul.o 13M 8 11l

a belt_s PI#3

FEF 12r P Cs#2 M1-HL SMAr MI#1 46d F4 PrCO CMA#2 MI-of VLo SII-f PC#1 X MI-body MDdc PN PIl PIm VPLc

VLc PIl-s PIc 6Va MDfi PIp

PMm VLm MDmf T

8Ad PMl 6Vb h VPM

4a 45A FD#1

VPLo Tha a

VLps

9/46d VApc PLd l

M2-FL D9 a

4b 4c ProM#2 belt_sm PLa#1 m PLvl

VL MDpm M2-HL 10m

PLvm u Gu VPI MDcd s

47/12 MDl SMAc

44 VPS 45B

6b-beta 9/46v VN

PFCorb 8Ac VAdc

OFap VP#2

14O

10v

46dr 46vr

OFO

10d

e 46f

n o r F

Fig. S32. The vertex positions are identical to that in Figure S31. The vertices are colored according to betweenness centrality where hot colors represent high betweenness centrality and cool colors indicate low betweenness centrality. It can be clearly seen that hot colors are concentrated in the inner rings.

38 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh obe ral L mpo ST1 Te A1

TPOc

Tpt ST3 TAa O cc

ST2 TH ip it AITv a l PrS L o b

PIT AITd e

TPO

36c Bla 36r

a TE l ENT Abpc u 35 Iam V4 B s STS Iapm Bi a n TPPro I Iai s TF a Idg B#2 l TG ABmg Ig#1 Ia#2 G e t a 36 a 25 n l Ldi g u l g i a n Lvl i Lv 23c C 23 L#2 SI#2 24b 24a 24 24c Cd PECg Pu_r 31 PGm PEc#1 SPL PEm

MIP e

b LIP o

L 7b IPL 7#1 PF#1

l 7a

i PG#1 Cl#2 CM#2

r Pcn

a S2 P Pul#1

Li 6#1 PM#3 M1 6M MD PL#3

2#1 8

F3 T

M1-FL h

MDmc Pul.o 6D a

F6 FEF MDpc a

F2 6V VPL m 46

8A u VA s 45 F7 14

F5 13 SMAr F4 12 10 9 VLo

13M

10o

46d

M9 PrCO 11l

13L

32 VAmc

46v

12l

12m

e 14r

o 13a

L PS

t 11m n 12r

12o o r F

Fig. S33. Vertices in the innermost core are shown. Vertices corresponding to the task-positive network are shown in red, vertices corresponding to the task-negative network are shown in blue, and the remaining vertices in the innermost core are shown in yellow. The vertex positions are identical to that in Figure S6.

39 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Fig. S34. A graph of how the core size decreases linearly with increasing k. A linear least-squares regression ﬁt is shown with (core size) = −8.0476∗k+380.9379.

40 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Table S1: Hierarchical brain map in depth-ﬁrst order

Level Acronym Full Name [Merged Brain Regions] Ring Degree Number Number Num- of of Con- ber times nec- studied tions reported 0 Br Brain according to GM-Deﬁnition 0 0 3 0 1 DiE Diencephalon according to GM-Deﬁnition 4 0 1 0 2 Hyp Hypthalamus 10 25 9 50 [ ALH APH DMH Hce1 Hce2 SMH hy ] 2 Tha Thalamus 5 1 2 1 3 AN Anterior nuclei of the thalamus 8 8 6 11 [ LN ] 4 LD#1 Laterodorsal nucleus (thalamus) 9 14 17 15 [ Cld ] 4 AV Nucleus anterior ventralis thalami 11 7 15 7 4 AM#1 Nucleus anterior medialis thalami 10 22 16 23 [ AMdc ] 4 AD#1 Nucleus anterior dorsalis thalami 9 5 10 5 3 ML Midline nuclei of the thalamus 7 12 14 18 [ Pac#2 sPFmc sPFpc ] 4 Re Nucleus reuniens thalami 11 24 14 26 [ Rv ] 4 PT#2 Nucleus parataenialis thalami 10 7 5 7 4 PAa Nucleus paraventricularis thalami, pars anterior 9 13 13 16 [ PAm#2 PAp Pa#3 ] 4 C#4 Nucleus centralis thalami 8 4 4 4 [ Ce#2 CeM#2 ] 5 Clc Nucleus centralis latocellularis thalami 11 11 7 12 5 Cim Nucleus centralis intermedialis thalami 10 7 5 7 5 Cif Nucleus centralis inferior thalami 9 11 8 11 5 Cdc Nucleus centralis densocellularis thalami 11 17 10 19 [ ND ] 3 GN Metathalamus (Geniculate Nucleii) 8 0 1 0 4 MG Corpus geniculatum mediale 10 23 59 49 [ AD#3 GM GMpc MC MGM MGN MGad ] [ MGpd PD#3 V Z ] 4 LGN dorsal Lateral geniculate nucleus 9 10 78 86 [ 2#2 DLG DLGN LGN#1 LGN 0 LGN 1 ] [ LGN 2 LGN 3 LGN 4 LGN 5 LGN 6 LGN il LGN il-z ] [ LGN k1 LGN l LGN mc LGN mc-il LGN mc-l LGN pc LGN pc-il ] [ LGN pc-l LGN s LGil LGm LGp LGs ] 3 IL#2 Intralaminar nuclei of the thalamus 7 14 5 14 4 Pf#2 Nucleus parafascicularis thalami 11 32 13 33 4 Pcn Nucleus paracentralis thalami 10 50 14 69 [ Pc#3 ] 4 CM#2 nucleus centrum medianum (thalamus) 9 43 24 71 [ CnMd ] 4 Cl#2 Nucleus centralis lateralis thalami 8 50 21 74 5 Csl Nucleus centralis superior lateralis thalami 11 28 8 31 5 Cs#2 Nucleus centralis superior thalami 10 5 6 5 3 MI#1 Massa intermedia 9 3 3 3 3 PN Posterior Nucleii of Thalamus 8 2 10 3 [ Po#5 SM ] 4 SG Nucleus suprageniculatus thalami 11 29 15 33 4 Li Nucleus limitans thalami 10 43 13 46 [ Lim ] 3 Ret Nucleus reticularis thalami 9 31 27 32 [ NRT AnteriorPole R#4 RT#2 ] 3 Pul#1 Nucleus pulvinaris thalami 7 44 32 137 [ PLe ] 4 PI#3 Nucleus pulvinaris inferior thalami 8 26 43 53 [ Pul.i ] 5 PIl-s Nucleus pulvinaris inferior thalami, shell of the lateral subdivision 11 2 3 2 5 PIp Nucleus pulvinaris inferior thalami, posterior subdivision 10 4 8 4 5 PIm Nucleus pulvinaris inferior thalami, pars medialis 9 7 9 7 5 PIl Nucleus pulvinaris inferior thalami, lateral subdivision 11 9 8 10 [ PIcl ] 5 PIc Nucleus pulvinaris inferior thalami, central subdivision 10 9 9 9 [ PIcm ] continued on next page...

41 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh ...continued from previous page Level Acronym Full Name [Merged Brain Regions] Ring Degree Number Number Num- of of Con- ber times nec- studied tions reported 4 PM#3 Nucleus pulvinaris medialis thalami 8 85 41 114 [ PMm-c Plm#2 Pul.m mPul ] 5 PMm Nucleus pulvinaris medialis thalami, medial division 9 7 1 7 5 PMl Nucleus pulvinaris medialis thalami, lateral division 11 8 1 8 4 Pul.o Nucleus pulvinaris oralis thalami 10 45 26 54 [ PO#3 Pa#4 Pla#2 ] 4 PL#3 Nucleus pulvinaris lateralis thalami 8 50 44 84 [ PLb PLi Pll#2 Pul.l ] 5 PLa#1 Nucleus pulvinaris lateralis thalami pars alpha 9 2 3 17 5 PLd Nucleus pulvinaris lateralis thalami, dorsal division 11 5 1 5 5 PLvl Nucleus pulvinaris lateralis thalami pars ventrolateralis 10 5 1 5 5 PLvm Nucleus pulvinaris lateralis thalami pars ventromedialis 9 5 3 5 3 MD Nucleus medialis dorsalis thalami 7 106 29 200 4 MDdc Nucleus medialis dorsalis thalami, pars densocellularis 11 21 8 23 [ MDd ] 4 MDcd Nucleus medialis dorsalis thalami, pars caudodorsalis 10 5 1 9 4 MDl Nucleus medialis dorsalis thalami, pars lateralis 8 6 2 6 5 MDpc Nucleus medialis dorsalis thalami, pars parvocellularis 9 38 10 43 5 MDmf Nucleus medialis dorsalis thalami, pars multiformis 11 17 8 18 4 MDmc Nucleus medialis dorsalis thalami, pars magnocellularis 8 39 12 57 [ MDm ] 5 MDpm Nucleus medialis dorsalis thalami, pars paramediana 10 10 1 10 5 MDfi Nucleus medialis dorsalis thalami, pars fibrosa 9 21 1 22 3 VN Ventolateral Nucleii of Thalamus 6 7 7 7 [ VM#2 VMH ] 4 X Area X (thalamus) 11 28 10 49 4 VP#2 Nucleus ventralis posterior 7 1 4 1 5 VPS Ventroposterior superior nucleus thalami 10 7 1 8 5 VPI Nucleus ventralis posterior inferior thalami 9 12 16 16 5 VPM Nucleus ventralis posterior medialis thalami 11 20 32 40 [ VPM CP VPM UL VPMpc n.vent.post.med. ] 5 VPL Aentral posterior lateral nucleus (thalamus) 8 56 39 88 [ LP VLp ] 6 VPLo Nucleus ventralis posterior lateralis thalami, pars oralis 10 20 11 48 6 VPLc Nucleus ventralis posterior lateralis thalami, pars caudalis 9 29 16 54 [ VPLc core h VPLc shell l ] 4 VL ventral lateral nucleus (thalamus) 8 18 9 19 5 VLm Nucleus ventralis lateralis thalami, pars medialis 11 25 10 43 5 VLps Nucleus ventralis lateralis thalami, pars postrema 10 21 7 25 5 VLo Nucleus ventralis lateralis thalami, pars oralis 9 34 11 68 [ VLa ] 5 VLc Nucleus ventralis lateralis thalami, pars caudalis 11 32 15 70 [ VLc-VPLo VLcc VLcr ] 4 VA ventral anterior nucleus (thalamus) 8 33 18 41 [ VAvm ] 5 VApc Nucleus ventralis anterior thalami, pars parvocellularis 10 21 8 38 5 VAdc Nucleus ventralis anterior thalami, pars densocellularis 9 7 1 7 5 VAmc Nucleus ventralis anterior thalami, pars magnocellularis 11 38 13 51 1 Cx GM-CerebralCortex 1 0 1 0 2 FL#2 FrontalLobe according to GM-Definition 4 0 1 0 3 belt sm belt line of the sensorymotor system according to CP99 10 22 2 22 [ root sm ] 3 Pfc Prefrontal Cortex 5 0 2 0 4 PFCorb Orbital prefrontal cortex 7 10 12 14 [ OF OFdg OFg OPro OrbPro ] 5 14 Orbitofrontal area 14 8 111 34 158 [ M14 ] 6 14O Orbital part of area 14 9 5 2 6 6 14r Rostral area 14 11 66 3 77 5 OFap Orbitofrontal cortex, agranular periallocortical 10 8 12 8 [ OFa-p PAll#1 ] 5 OFO Orbitofrontal opercular area 8 2 6 2 6 ProM#2 Pro motor area 9 31 8 33 [ proM#1 ] 6 Gu Gustatory cortex 11 22 16 25 continued on next page...

42 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh ...continued from previous page Level Acronym Full Name [Merged Brain Regions] Ring Degree Number Number Num- of of Con- ber times nec- studied tions reported [ G#1 G#2 G#3 ] 5 13 Orbitofrontal area 13 8 129 36 203 [ FF ] 6 13L Orbitofrontal area 13, lateral part 10 47 5 55 6 13M Orbitofrontal area 13, medial part 9 39 5 55 6 13a Orbitofrontal area 13a 11 130 15 223 [ 13b ] 4 32 Area 32 10 159 36 226 4 FD#1 Prefrontal area FD 6 33 2 42 5 10 Area 10 8 100 39 154 [ M10 ] 6 10m Medial area 10 9 21 4 24 6 10v Ventral area 10 11 7 3 10 [ V10 ] 6 10d Dorsal area 10 10 3 3 7 [ D10 ] 6 10o Orbital area 10 9 44 2 52 5 12 Area 12 8 90 31 136 6 12o Orbital area 12 11 135 10 174 [ O12 ] 6 12m Medial area 12 10 54 2 69 6 47/12 Prefrontal area 47/12 9 24 7 27 [ 47/12L 47/12O ] 6 12r Rostral area 12 11 38 2 47 6 12l Lateral area 12 10 123 9 155 [ 12vl L12 ] 5 11 Area 11 8 127 33 207 6 11l Lateral area 11 9 39 4 52 6 11m Medial area 11 11 63 4 76 5 9 Area 9 8 125 53 219 [ 9d 9m ] 6 L9 Lateral area 9 10 7 1 9 6 M9 Medial area 9 9 43 1 51 6 D9 dorsal area 9 11 26 1 30 5 46 Cortical area 46 7 211 46 366 [ 46inf 46p 46sup FDdelta ] 6 46v Ventral area 46 10 89 12 120 [ V46 V46r ] 6 46d Dorsal area 46 9 45 11 58 [ D46 D46r ] 6 PS Principal Sulcus 11 70 1 72 6 46f Area 46 (fundus of the principal sulcus) 10 2 1 2 6 46vr Area 46 (ventral rim of the principal sulcus) 9 5 3 5 6 46dr Area 46 (dorsal rim of the principal sulcus) 11 4 2 4 6 9/46 Cortical area 9/46 8 0 2 0 7 9/46v Cortical area 9/46v 10 13 3 15 7 9/46d Cortical area 9/46d 9 30 3 36 4 8 Area 8 6 54 32 85 [ 8As ] 5 FEF Frontal eye ﬁeld 7 67 13 93 6 45 Cortical area 45 8 79 32 100 [ 8v FDgamma V8#2 ] 7 45A Cortical area 45A 11 31 9 43 [ 45a+8Ar 8Ar ] 7 45B Cortical area 45B 10 12 5 14 6 8A Area 8A 8 97 17 133 [ 8Av ] 7 8Ad Dorsal portion of area 8A 9 29 3 32 7 8Ac Caudal area 8A 11 6 4 7 5 8B Area 8B 10 89 23 116 [ 8Bd 8Bm 8d D8 ] 3 6#1 Area 6 6 70 50 114 [ 6a-alpha 6a-beta 6b FB PM#4 ] 4 6V Area 6 (ventral part) 8 74 12 258 [ PMCvl PMv V6#2 vPmC ] continued on next page...

43 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh ...continued from previous page Level Acronym Full Name [Merged Brain Regions] Ring Degree Number Number Num- of of Con- ber times nec- studied tions reported 5 F5 Agranular frontal area 5 (= rostral ventrolateral premotor area) 9 88 16 137 [ 6VR FCBm MLA PMv-r PMvr ] 5 PrCO Precentral opercular area 11 36 16 51 [ 6b-alpha ] 5 4c Motor area 4c 10 17 7 20 [ Postarc ] 5 6Vb Premotor area 6Vb 9 20 9 23 5 6Va Premotor area 6Va 11 23 10 25 [ 6Vam 6val ] 5 F4 Agranular frontal area 4 (= caudal ventrolateral premotor area) 10 48 13 84 [ 6VC FBA PMv-c PMvc ] 4 44 Cortical area 44 9 6 4 6 4 6b-beta Premotor area 6b-beta 11 2 2 2 4 6D Premotor area 6 (dorsal part) 8 82 22 151 [ 6Ds D6 PMd dPmC ] 5 F7 Agranular frontal area 7 (= rostral dorsolateral premotor area) 10 124 28 245 [ 6DR F7-SEF F7-nonSEF PMd-r PMdr SEF rPMd ] 5 F2 Agranular frontal area 2 (= caudal dorsolateral premotor area) 9 88 22 183 [ 6DC F2d F2vr PMd-c PMdc Pmdp cPMd ] 4 6M Medial premotor area 6M 7 93 50 188 [ M2 M2-FA MII MII-arm MII-face MII-leg MII-trunk PMCm ] [ SMA SMA-of TMA ] 5 F3 Agranular frontal area 3 (= SMA-proper) 8 69 15 162 [ F3-arm F3-axial F3-leg SMA-proper ] 6 SMAr SMA - rostral part 11 41 1 43 6 SMAc SMA - caudal part 10 2 1 2 5 M2-HL Supplementary motor cortex M2, hindlimb area 9 7 1 15 5 M2-FL Supplementary motor cortex M2, forelimb area 11 6 1 13 5 F6 Agranular frontal area 6 (= pre-SMA) 10 57 17 108 [ F6-arm F6-axial pre-SMA preSMA ] 3 M1 Primary motor area 8 96 57 246 [ 4#1 F1 FA MI#3 ] 4 M1-FL Primary motor cortex M1, forelimb area 9 86 16 164 [ 4-fl 4-hand ARM F1-arm MI-arm MI-finger MI-forelimb ] [ MI-hand MI-hand-arm ] 4 MI-of orofacial representation in MI 11 24 5 34 [ 4-mouth F1-face M1-FA ] 4 4b Motor area 4b 10 2 1 2 4 4a Motor area 4a 9 2 1 2 4 MI-body body representation of MI as defined in KSI03 11 21 4 28 [ M1-AX MI-neck MI-trunk ] 4 M1-HL Primary motor cortex M1, hindlimb area 10 31 6 44 [ F1-leg MI-hindlimb MI-leg MI-toe ] 2 Pl#6 ParietalLobe according to GM-Definition 5 0 1 0 3 S1 Primary somatosensory cortex 7 31 39 68 [ 1-2 SI#1 SI-arm SI-finger SI-leg SI-neck SI-trunk ] [ SI D1 SI D1p SI T3-4 SI Trnk ] 4 PC#1 Primary sensory area PC 8 14 3 18 [ 3b/1 ] 5 1#1 Area 1 9 49 46 149 [ 1 O SI Arm SI Hnd SI LL SI Max SI T1 SI T4-5 ] [ SI UL SI ULp ] 5 2#1 Area 2 11 54 43 153 [ 2 D2-5 SI D2 SI D2-3 SI D2-3p SI D2-4 SI D3-4 SI D3-4p SI D3-5 ] 4 3#1 Area 3 8 27 14 33 5 3b Postcentral area 3b 10 32 28 75 [ 3b CP 3b LL 3b UL SI Leg ] 5 3a Postcentral area 3a 9 35 26 67 3 S2 Secondary somatosensory cortex 8 81 56 206 [ 43 PCop SII SII-fl SII-h SII-hl SII-sub ] 4 SII-f face representation in SII as defined in DLRPK03 11 5 3 13 4 CMA#2 Cortical masticatory area 10 2 4 2 [ CMAaAd CMAp ] 3 belt s belt line of the sensory system according to CP99 9 13 1 21 3 PR#4 rostroventral parietal area as defined in DLRPK03 11 19 6 54 continued on next page...

44 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh ...continued from previous page Level Acronym Full Name [Merged Brain Regions] Ring Degree Number Number Num- of of Con- ber times nec- studied tions reported [ PV#2 PV-f PV-fl PV-h ] 3 7#1 Area 7 6 63 17 133 [ 7t VS root s ] 4 PFop Rostral parietal operculum 10 9 6 20 4 PP Posterior parietal area 9 3 3 3 4 PGop Caudal parietal operculum 11 13 10 15 [ 7op ] 4 IPL Inferior Parietal Lobule 7 68 7 101 [ 7a/7b PCi ] 5 7a Area 7a 8 52 29 74 6 PG#1 Caudal inferior parietal lobule 10 77 28 104 [ PGc PGlat PGmed SPG ] 6 Opt Occipitoparietal area 9 38 10 46 5 7b Area 7b 8 92 29 143 6 PFG#1 Midpart of the inferior parietal lobule 11 38 8 47 6 PF#1 Rostral inferior parietal lobule 10 54 13 73 3 PCip Cortex of the intraparietal sulcus 7 0 2 0 4 LIP Lateral intraparietal area 8 128 33 207 [ 7ip LIPd+LIPv POa ] 5 LIPe Lateral intraparietal area (external part) 9 15 10 19 [ LIPd POa-e ] 5 LIPi Lateral intraparietal area (internal part) 11 18 11 21 [ LIPv POa-i ] 4 VIP Ventral intraparietal area 10 43 34 64 [ IPd VIPl VIPm ] 4 PIP#1 Posterior intraparietal area 9 17 7 21 4 AIP Anterior intraparietal area 11 14 9 20 4 MIP Medial intraparietal area 10 50 23 83 [ 5ip PEa PEip ] 3 PCd#2 Dorsal parietal cortex (= SPL and precuneus) 7 0 2 0 4 SPL Superior Parietal Lobule 8 46 37 100 [ 2/5 5D 5V 5m ] 5 PEm Rostral superior parietal lobule 9 57 14 87 [ PE#1 PE#2 ] 5 5 Foot Receptive field for the foot in Area5 11 4 1 4 5 PEc#1 Caudal and medial superior parietal lobule 10 58 11 82 [ 5b PEc#2 PEp ] 4 PCm Medial parietal cortex (= Precuneus) 8 0 2 0 5 PGm Parietal area PG, medial part 9 107 17 149 [ 7m#1 MDP ] 5 31 Area 31 11 54 11 64 5 PECg Parietal area PE (cingulate part) 10 61 9 72 [ SSA ] 2 CgG#2 Cingulate Gyrus according to GM-Definition 6 0 2 0 3 24 Anterior cingulate area 24 8 176 55 383 [ LA#1 ] 4 24c Area 24c (rostral part of the cingulate sulcus) 9 77 28 135 [ 24c-arm 24c-d 24c-l 24c-m 24c-v M3 ] 4 24d Area 24d (rostral part of the cingulate sulcus) 11 27 23 48 [ 24d-arm 24d-leg CMAr ] 4 24b Area 24b 10 67 16 100 4 24a Area 24a 9 47 15 76 3 23 Area 23 8 82 37 169 [ CGp LC#1 ] 4 23c Area 23c 11 88 43 198 [ 23c-d 23c-l 23c-m 23c-v 6c CMAc CMAd#1 ] [ CMAv M4 ] 4 23b Area 23b 10 33 9 55 4 TSA Transitional sensory area 9 25 1 29 4 23a Area 23a 11 19 9 31 3 26 Area 26 7 5 12 6 [ RSpC Rsp rspl-c ] 4 29 Area 29 8 15 14 20 5 CML Caudomedial lobule 10 2 1 2 5 29d Area 29d 9 9 9 12 continued on next page...

45 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh ...continued from previous page Level Acronym Full Name [Merged Brain Regions] Ring Degree Number Number Num- of of Con- ber times nec- studied tions reported [ 29m ] 5 29a-c Cortical area 29a-c 11 20 20 50 [ 29a 29b 29c 29l ] 4 30 Retrosplenial area 30 10 20 17 30 [ 30d 30pv ] 3 25 Area 25 9 82 44 142 [ 14c FL ] 2 Insula Insula 6 52 5 66 [ I#3 I#3m INS PI#2 ] 3 Ig#1 Granular insular cortex 11 48 26 86 [ GI Ip#3 ] 3 Ri#1 Retroinsular area 10 22 24 44 [ reIpt reIt ] 3 IPro Insular proisocortex 9 3 2 3 [ IP#2 ] 3 Pi#1 Parainsular field/cortex 11 34 16 40 [ paI#1 ] 3 IA#1 Anterior insula 7 0 4 0 4 Idg Dysgranular insular cortex 10 58 20 76 [ DI#2 Id ] 4 Ia#2 Agranular insula 8 37 16 47 [ AI#2 Ia-p Iac Iag ] 5 Ial Lateral agranular insular cortex 9 23 5 42 [ Iapl ] 5 Iam Medial agranular insular cortex 11 49 5 67 [ Iav ] 5 Iapm Posteromedial agranular insular cortex 10 51 2 61 5 Iai Intermediate agranula insular cortex 9 86 3 120 [ Iad ] 2 TL#2 Temporal Lobe according to GM-Definition 2 0 1 0 3 TCv Ventral Temporal Cortex 3 0 2 0 4 TF Temporal area TF 8 127 54 199 [ TFO VTF ] 5 TFM Temporal area TF (medial part) 11 35 7 40 [ TF2 ] 5 TFL Temporal area TF (lateral part) 10 43 7 47 [ TF1 ] 4 Per#1 Perirhinal cortex 4 12 4 12 [ Peri Pr#2 ] 5 35 Area 35 9 74 57 136 [ 35-I 35-II 35-III 35-IV 35-V 35-VI 35a ] 5 36 Area 36 5 95 42 176 [ 36-I 36-II 36-III 36-IV 36-V 36-VI 36/TF/TE ] 6 36c Caudal part of area 36 11 53 22 68 [ 36cl TLO TLc ] 6 36r Rostral part of area 36 10 83 19 130 [ 36rm TLR ] 6 TG Temporopolar area TG 6 96 18 134 7 TPPro Temporal proisocortex 7 49 23 71 [ 36d Pro#1 TempPro ] 8 TPag Agranular area of temporal polar cortex 9 17 4 25 [ TPa-p ] 8 TPg Granular area of temporal polar cortex 11 24 3 34 8 TPproD Dysgranular Temporopolar Cortex 8 15 5 23 [ DLP DMP TPdg ] 9 TPdgv Ventral dysgranular area of temporal polar cortex 10 10 2 13 9 TPdgd Dorsal dysgranular area of temporal polar cortex 9 10 2 13 7 36p Cortical area 36p 11 14 4 19 [ 36pl 36pm ] 3 PHC Parahippocampal cortex 6 8 4 13 [ PH paraHC ] 4 ENT Entorhinal cortex 7 92 61 176 [ 28 28-I 28-II 28-III 28-V 28-VI 28-iv E EC#1 ER#2 ] 5 EL Lateral field of entorhinal cortex 8 27 20 32 [ 28L 28b Pr#1 ] continued on next page...

46 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh ...continued from previous page Level Acronym Full Name [Merged Brain Regions] Ring Degree Number Number Num- of of Con- ber times nec- studied tions reported 6 ELr Lateral field (rostral part) of entorhinal cortex 10 21 13 23 [ Pr1 ] 6 ELc Lateral field (caudal part) of entorhinal cortex 9 10 14 17 [ 28S-I 28S-III 28S-V 28s ] 5 EI Intermediate field of entorhinal cortex 11 37 18 49 [ 28I-III 28i ] 5 ER#1 Rostral field of entorhinal cortex 10 26 6 30 5 28m medial entorhinal cortex 9 15 12 22 [ 28M-III 28a ] 5 EO Olfactory field of entorhinal cortex 11 17 6 18 5 ECL Caudal limiting field of entorhinal cortex 10 21 6 28 5 EC#2 Caudal field of entorhinal cortex 9 44 6 62 4 S#1 Subiculum 8 32 38 46 [ S-SM S-SP Sub Subr ] 5 Su#2 Subiculum, uncal portion 11 5 1 6 5 Sb Subiculum, body portion 10 5 1 6 4 Pros. prosubiculum 9 26 34 34 [ PoS ProS#2 ProS-SM ProS-SP ] 4 PaS Parasubiculum 11 22 24 23 [ ParaS ] 4 TH Temporal area TH 10 110 48 158 [ THO THc THr ] 4 PrS Presubiculum 9 39 38 46 [ 27 PreS PreS-Lpe Psb Psub ] 3 Hip Hippocampus 8 24 66 39 [ CA2 CA2-SLM CA4 H#1 HF h#3 ] 4 CA1 CA1 subfield of Ammon‘s horn 11 45 87 116 [ CA1-SLM CA1-SM CA1-SP CA1-SR CA1a CA1med-sm ] [ CA1med-sp CA1med-sr CA1t’ CA1t’-SP ] 4 DG dentate gyrus 10 10 31 17 [ DG-gc DG-ml ] 4 CA3 CA3 subfield of Ammons horn 9 12 44 15 [ CA3-SLM ] 3 STG superior temporal gyrus 5 29 10 61 [ 22 STGf STGi STGm STGo ] 4 STP#2 Supratemporal plane 6 0 1 0 5 A1 Primary auditory cortex 11 49 40 109 [ KA R#2 RA RP paAr ] 5 STPg Supratemporal cortex, granular 10 24 1 24 5 A2 Secondary auditory cortex 7 33 9 40 [ AII belt ] 6 Pa#2 Postauditory field 8 11 12 22 [ CM#1 P-m RTM ] 7 ProK auditory prokoniocortex 9 19 11 32 [ A-m RM proA ] 7 paAc Caudal auditory parakoniocortex 11 28 6 42 [ CP ] 6 paAlt Lateral auditory parakoniocortex 8 40 17 91 [ RTL lateral-belt ] 7 L#1 Lateral auditory field 10 33 7 54 [ LA#2 ML#1 PL#5 ] 7 CL#4 cudal lateral auditory (belt) 9 23 5 32 [ Toc#2 ] 7 AL#4 anterior lateral auditory belt 11 21 3 27 4 TA Temporal area TA 7 28 13 49 [ STGa STGp#1 ] 5 Ts Area temporalis superior 8 0 2 0 6 ST3 Superior temporal area 3 10 57 20 76 [ 3#3 4#3 STGl STGr Ts3 ] 6 ST2 Superior temporal area 2 9 50 16 65 6 ST1 Superior temporal area 1 11 39 16 47 5 Tpt Temporoparietal cortex 10 50 16 61 3 TE Inferotemporal area TE 6 115 45 222 [ IT TEO+TE TEO+TE+TE3 tmps ] 4 20 Area 20 7 19 9 28 continued on next page...

47 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh ...continued from previous page Level Acronym Full Name [Merged Brain Regions] Ring Degree Number Number Num- of of Con- ber times nec- studied tions reported [ ITi TE1-3 TEv ] 5 AITv Anterior inferotemporal area (ventral) 9 68 19 102 [ TE1#1 TE1#2 TEav ] 5 CIT Central inferotemporal area 8 29 7 38 [ TEpv ] 6 CITd Central inferotemporal area (dorsal) 11 11 14 13 [ TE3#1 ] 6 CITv Central inferotemporal area (ventral) 10 36 13 39 [ TE2#1 TE2#2 ] 4 21 Area 21 7 12 9 14 [ ITm ] 5 AITd Anterior inferotemporal area (dorsal) 8 57 11 80 [ STSv TEa/m TEad TEm/TEa ] 6 TEa#3 anterior part of area TE 9 30 18 34 [ TEa#1 TEa#2 ] 6 TEm Cortical area TEm 11 14 15 18 5 PIT Posterior inferotemporal area 8 112 47 216 [ TEO TEO+ TEp TEpd ] 6 PITd Posterior inferotemporal area (dorsal) 10 18 8 25 [ TEOd ] 6 PITv Posterior inferotemporal area (ventral) 9 20 4 20 [ TEOv ] 3 STS Superior temporal sulcus 6 54 7 117 [ ST STP#1 ] 4 STSd Superior temporal sulcus, dorsal 7 25 2 28 5 TPO Temporal parietooccipital associated area in the STS 8 72 15 98 6 TPOc Temporoparietal asscociated area (caudal part) 11 51 14 67 [ STPp TPO3 TPO4 ] 6 TPOi Temporoparietal associated area (intermediate part) 10 6 2 6 6 TPOr Temporoparietal associated area (rostral part) 9 30 12 46 [ STPa TPO1 TPO2 ] 5 TAa Temporal area TAa 11 45 12 58 4 STSf Superior temporal sulcus, fundus 8 0 1 0 5 PGa Cortical area PGa 10 36 13 48 5 IPa Intraparietal sulcus associated area in the STS 9 37 17 47 4 OAa Cortical area OAa 7 15 7 21 5 MT Middle temporal area 11 75 52 113 [ V5 V5a ] 5 MTp Peripheral part of area MT 10 8 7 8 5 FST Floor of superior temporal sulcus 9 48 23 73 5 MST Medial superior temporal area 8 22 36 27 [ DMZ MSTm ] 6 MSTp Medial superior temporal area (posterior) 11 20 3 20 6 MSTd Medial superior temporal area (dorsal) 10 49 6 70 [ MSTc MSTda MSTdp ] 2 OC#2 OccipitalLobe according to GM-Deﬁnition 4 0 5 0 3 VAC Visual anterior cortex 5 0 2 0 4 OA Extrastriate area OA 6 38 27 71 [ 19 ] 5 V3A Visual area 3A 9 32 24 47 5 V3 Visual area 3 8 35 29 46 [ region-2 ] 6 V3d Dorsal visual area 3 11 8 14 12 6 V3v Ventral visual area 3 10 38 27 68 [ VP#1 ] 5 V4 Visual area 4 7 78 50 138 [ region-3 region-4 region-6 region-7 ] 6 V4t V4 transitional area 9 26 24 35 [ V4ta V4tp region-5 ] 6 V4d Visual area 4 (dorsal part) 8 18 7 23 [ DL#1 ] 7 DLr dorsolateral visual cortex, rostral part 11 2 2 4 7 DLc dorsolateral visual cortex, caudal part 10 2 2 4 6 V4v Visual area 4 (ventral part) 9 6 6 8 5 VPP Ventral posterior parietal area 11 2 2 3 continued on next page...

48 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh ...continued from previous page Level Acronym Full Name [Merged Brain Regions] Ring Degree Number Number Num- of of Con- ber times nec- studied tions reported 5 DI#1 dorsointermediate visual ﬁeld 10 2 2 4 5 PO#4 medial visual association area 8 35 21 48 [ M#3 PO#1 ] 6 V6A Visual area V6A 9 33 6 48 6 V6 Visual area 6 11 41 10 57 [ DM#1 ] 5 DP Dorsal prelunate gyrus 10 36 16 40 [ DPL ] 4 VOT Ventral occipitotemporal area 9 7 3 9 3 V1 Visual area 1 11 47 113 158 [ 17 17 I LVQ OC StriateC StriateC-I StriateC-II StriateC-III ] [ StriateC-IV UVQ V1 I V1 II V1 III ] 3 ProSt Prostriate cortex 10 3 3 3 [ P#4 PRO ] 3 V2 Visual area 2 9 82 68 205 [ 18 OB V2 clf V2 ilf V2 iuf V2 puf V2d V2v ] [ region-1 v2(+) v2(-) v2(0) ] 1 BG Basal Ganglia according to GM-Deﬁnition 5 0 1 0 2 Amyg Amygdala 6 23 17 49 [ amg ] 3 B#2 basal amygdaloid nucleus 8 65 56 91 [ AB#2 ABa ACC-B Amyg AB B#4 BA ] 4 Bla Basolateral nucleus of amygdala 11 53 27 68 [ ABl BL#2 Bl#1 LB ] 4 Abpc Accessory basal amygdaloid nucleus, parvicellular part 10 45 49 81 [ BAp BLp Bp Bpc Bpl PL#2 PL#4 ] [ PLl PLm ] 4 Bi Basal amygdaloid nucleus, intermediate part 9 43 10 50 4 ABd Accessory basal amygdaloid nucleus, dorsal division 11 23 2 45 [ Bd ] 4 Bvl Basal amygdaloid nucleus, ventral lateral division 10 19 1 27 4 ABv Accessory basal amygdaloid nucleus, ventral division 9 23 1 32 4 MB Medial basal nucleus of the amygdala 11 38 25 46 [ ABm BM#3 Bm#1 ] 4 ABvm Accessor basal nucleus (amygdala), ventromedial division 10 30 10 51 [ Abs Bvm ] 4 ABmg accessory basal nucleus (amygdala), magnocellular subdivision 9 49 32 82 [ BAm#1 BLm Bmc Bmg abmc ] 3 A anterior amygdaloid area 11 24 30 26 [ AA AAA ] 3 I#2 Intercalated amygdaloid nucleus 10 6 13 6 3 ME#1 Medial nucleus of the amygdala 9 25 38 31 [ M#1 ] 3 CE#1 central nucleus of the amygdala 11 26 61 50 [ C#2 CEl CEm#1 CEmc Cec Cl#3 Cm#3 ] 3 PAC#1 periamygdaloid cortex 7 25 26 36 [ APir PACo PACo#1 VCo VCoIf VCoIt VCoS ] 4 AHA amygdalohippocampal area 10 16 43 21 [ AHAd AHAv HATA ] 4 PAC2 Periamygdaloid cortex 2 9 21 44 52 [ BPACs CTA PAC1 PAC3 PACs pam#1 ] 4 Co cortical nucleus (amygdala) 8 10 21 13 [ Amyg CO CN ] 5 COp cortical nucleus, posterior division 11 12 14 14 5 NLOT Nucleus of the lateral olfactory tract 10 9 13 9 5 COa cortical nucleus, anterior division 9 14 16 15 3 L#2 lateral nucleus, amygdala 7 86 40 134 [ Amyg L LAT LT ] 4 Ldm Lateral amygdaloid nucleus, dorsomedial region 8 0 2 0 5 Ldi Lateral nucleus (amygdala), dorsal intermediate division 11 58 4 69 5 Ld#2 Lateral nucleus (amygdala), dorsal division 10 35 4 43 4 Lv Lateral nucleus (amygdala), ventral division 9 52 4 68 4 Lvl lateral nucleus (amygdala), ventrolateral subdivision 11 43 7 50 2 SN substantia nigra 10 8 6 8 [ SN.com SN.ret ] continued on next page...

49 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh ...continued from previous page Level Acronym Full Name [Merged Brain Regions] Ring Degree Number Number Num- of of Con- ber times nec- studied tions reported 2 SI#2 substantia innominata 9 55 19 194 [ Acc#1 Acc-core Ch1 Ch2 Ch3 Ch4 Ch4al Ch4am ] [ Ch4id Ch4iv Ch4p MS NBM NVDB VP#3 ] 2 Sub.Th Nucleus subthalamic 11 3 6 3 [ ZI Zic ] 2 GPe Globus pallidus, external part 10 4 6 7 [ GPi ] 2 STR striatum 7 0 1 0 3 Cd Nucleus caudatus 8 52 123 237 [ Cd b Cd b i c Cd b i d Cd b i v Cd b l c Cd b l d ] [ Cd b l v Cd b m c Cd b m d Cd b m v Cd h Cd h i c Cd h i d ] [ Cd h i v Cd h l c Cd h l d Cd h l v Cd h m c Cd h m d Cd h m v ] 4 Cd t Nucleus caudatus; tail 9 17 44 56 [ Cd t i c Cd t i d Cd t i v Cd t l c Cd t l d Cd t l v Cd t m c ] [ Cd t m d Cd t m v ] 4 Cd g Nucleus caudatus; genu 11 28 57 87 [ Cd g i c Cd g i d Cd g i v Cd g l c Cd g l d Cd g l v Cd g m c ] [ Cd g m d Cd g m v ] 3 Pu Putamen 8 20 46 43 [ Pu m i c Pu m i d Pu m i v Pu m l c Pu m l d Pu m l v Pu m m c ] [ Pu m m d Pu m m v ] 4 Pu r Putamen; rostral 10 46 50 122 [ Pu r i c Pu r i d Pu r i v Pu r l c Pu r l d Pu r l v Pu r m c ] [ Pu r m d Pu r m v ] 4 Pu c Putamen; caudal 9 27 49 72 [ Pu c i c Pu c i d Pu c i v Pu c l c Pu c l d Pu c l v Pu c m c ] [ Pu c m d Pu c m v ] 2 Clau Claustrum 11 25 17 26 [ CL#1 ] 1 MB#2 Mid Brain 10 20 81 99 [ APT CG DLT GPO NCS NOT NPA NPC ON ] [ PG#2 PPN#1 PPN#2 PPT#2 RTP SC SC I SC III SC II 1 SC II 2 ] [ SC II 3 SC IV SC V SC VI SC VII SL SZ Teg.a VLZ VTA ] 1 OFC Olfactory Complex 9 17 35 26 [ AON B-Olf OLF OT PC#2 POC Pir ]

The color of each row is derived from corresponding color in Figure S6.

50 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Table S2: A summary of number of connections in major brain pathways

DiE BG Cx DiE 10 10 953 BG 37 186 289 Cx 505 446 4129

Diencephalon (DiE), basal ganglia (BG), and cortex (Cx). The (i, j)-th entry shows number of connections from row i to column j, for example, there are 289 edges from BG to Cx and 446 edges from Cx to BG. There are 953 feedforward connections from thalamus to cortex, and 505 feedback connections from cortex to thalamus, thus reciprocity in these relays is only of the order of 34% as compared to 42% for the entire graph. We found 248 short loops of length 2 (thalamus to cortex and back) involving 55 thalamic regions and 60 cortical regions thus conﬁrming the pervasiveness of short thalamocortical loops [25, 18].

51 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Table S3: A summary of number of connections in major corticocortical pathways

DiE BG OC#2 Pl#6 TL#2 FL#2 CgG#2 Insula DiE 10 10 37 160 105 600 25 26 BG 37 186 8 8 140 95 14 24 OC#2 61 16 77 53 77 46 6 0 Pl#6 103 47 38 178 83 251 55 21 TL#2 92 172 60 99 684 388 70 28 FL#2 197 145 12 178 238 695 151 32 CgG#2 37 22 0 48 63 202 39 10 Insula 15 44 0 41 78 101 13 14 Num Areas 75 41 23 41 88 81 18 12 Avg In- 8.50 15.83 11.09 20.67 17.67 30.16 21.94 14.27 Degree Avg Out- 14.16 14.25 15.85 20.45 19.16 20.71 24.64 27.45 Degree

Diencephalon (DiE), basal ganglia (BG), and six cortical constituents: temporal lobe (TL#2), frontal lobe (FL#2), parietal lobe (Pl#6), occipital lobe (OC#2), insula (Insula), and cingulate cortex (CgG#2). The (i, j)-th entry shows number of connections from brain substructure in row i to brain substructure in column j. For each brain substructure, we show the number of its sub-regions (Num Areas), average in-degrees (the ratio of the total number of connections entering the substructure to the number of regions in it), and average out-degrees (the ratio of the total number of connections leaving the substructure to the number of regions in it). incoming links) and average out-degrees (deﬁned as the average number of outgoing links) and number of cortical areas in each column.

52 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Table S4: Brain regions associated with each ﬁber system are listed in the corresponding row

Fiber System Brain Regions Felleman-Van Essen [8] V1 V2 V3 V3v V3A V4 VOT V4t MT FST PITd PITv CITd CITv AITd AITv TPOc TPOr TF TH MSTd MSTp PO#4 PIP#1 LIP VIP MIP PGm DP 7a FEF 46 Dorsal Ventral [17] V2 ProSt V1 STS TE VOT OA OAa TH TF MIP AIP PIP#1 VIP LIP IPL DP PO#4 V4 V3 MST FST MTp MT IPa PGa TPO PIT AITv 36 TFL TFM PECg 31 PGm PEc#1 PEm LIPi LIPe 7a V6 V6A V4v V4d V4t V3v V3d V3A MSTd MSTp PITv PITd TEm CITv CITd Opt PG#1 Arcuate Fasciculus [19] TPO Tpt F2 F7 TPOr TPOc 8Ad 9/46d Cingulum Bundle [19] 25 PrS TH ENT TF 30 29 6M 6D 32 EC#2 ECL EO 28m ER#1 EI EL 36 35 TFL TFM 29a-c 29d 7a F6 F3 F2 F7 9 11 14 ELc ELr TG 36r 36c Opt PG#1 SMAc SMAr 46d D9 M9 L9 11m 11l 14r 14O 36p TPPro 8Ad 9/46d TPproD TPg TPag TPdgd Extreme Capsule [19] Insula Pi#1 Ri#1 Ig#1 24 TH Ia#2 Idg 24a 24b 24c 32 IPa TAa TPO 36 Iai Iapm Iam Ial TPOr TPOi TPOc ST2 ST3 paAlt TG 36r 36c 45 47/12 AL#4 CL#4 L#1 36p TPPro 8Ad 45B 45A 9/46d TPproD TPg TPag TPdgd TPdgv Fronto-Occipital Fasciculus 6D DP PO#4 PGm 7a F2 F7 8B 9 V6 V6A Opt PG#1 46d D9 M9 L9 8Ad [19] Inferior Longitudinal Fascicu- V2 V1 20 TH TF LIP DP V4 V3 MST FST MT IPa PIT CIT AITv 36 TFL TFM LIPi LIPe lus [19] V4v V4d V4t V3v V3d V3A MSTd MSTp PITv PITd TEa#3 CITv CITd TG 36r 36c Opt DLc DLr 36p TPPro TPproD TPg TPag Middle Longitudinal Fasciculus 23 TF 30 23a TSA 23b 23c DP IPa PGa TAa TPO Tpt A1 TFL 7a TPOr TPOi TPOc paAlt Pa#2 [19] Opt PG#1 AL#4 CL#4 L#1 paAc ProK Superior Longitudinal Fascicu- LIP PFop 6M 6D 44 6V 31 PGm PEc#1 PEm LIPi LIPe 7b 7a F6 F3 F2 F7 F4 6Va 6Vb 4c lus [19] PrCO F5 46 9 PF#1 PFG#1 Opt PG#1 SMAc SMAr 46dr 46vr 46f PS 46d 46v D9 M9 L9 8Ad 9/46d 9/46v Uncinate Fasciculus [19] Amyg L#2 PAC#1 CE#1 ME#1 I#2 A B#2 25 24 Lvl Lv Co PAC2 AHA ABmg ABvm MB ABv Bvl ABd Bi Abpc Bla TH ENT Per#1 TF 24a 24b 24c 32 Ld#2 Ldi COa NLOT COp IPa AITv EC#2 ECL EO 28m ER#1 EI EL 36 35 TFL TFM 11 10 13 14 TEa#3 ST1 ELc ELr TG 36r 36c 11m 11l 47/12 10o 10d 10v 10m 13a 13M 13L 14r 14O 36p TPPro TPproD TPg TPag TPdgd TPdgv

53 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Table S5: A core decomposition of the brain network into shells and ﬁner sub- shells Shell Fine Shell Brain Regions S0 F0,1 Br BG Cx DiE STR CgG#2 FL#2 OC#2 Pl#6 TL#2 Pfc IA#1 VAC PCd#2 PCip TCv GN Ldm PCm STP#2 STSf Ts 9/46 S1 F1,1 Tha VP#2 S2 F2,1 PN 4a 4b 6b-beta CMA#2 CML OFO DI#1 VPP PIl-s PLa#1 SMAc 46f DLc DLr S3 F3,1 Sub.Th IPro ProSt MI#1 PP 10d S4 F4,1 GPe C#4 5 Foot PIp 46dr S5 F5,1 26 SII-f AD#1 MDcd Sb Su#2 PLvm PLvl PLd Cs#2 14O 46vr S6 F6,1 I#2 44 MDl M2-FL V4v TPOi 8Ac S7 F7,1 VN VOT AV PT#2 M2-HL Cim PIm PMm VAdc VPS 10v L9 S8 F8,1 SN PHC AN OFap MTp PMl V3d S9 F9,1 PFop NLOT 29d PIc PIl S10 F10,1 Co PFCorb DG LGN MDpm ELc TPdgd TPdgv S11 F11,1 Cif Clc CITd Pa#2 S12 F12,1 ML CA3 21 Per#1 COp VPI 45B 9/46v S13 F13,1 belt s PGop PAa 28m 36p S14 F14,1 MB#2 IL#2 PC#1 AIP LD#1 COa TEm S15 F15,1 Cd t 29 OAa LIPe TPproD F15,2 PITd TPag S16 F16,1 OFC Bvl AHA EO F16,2 ABd ABv S17 F17,1 PR#4 PIP#1 4c MDmf Cdc V4d PITv F17,2 Amyg S18 F18,1 PAC2 VL LIPi ELr F18,2 MI-body 20 S19 F19,1 Pu 23a PaS ECL VPM VPLo ProK F19,2 Hip Gu S20 F20,1 A belt sm ABvm 30 29a-c 6Vb VLps 47/12 MSTp F20,2 ME#1 S21 F21,1 3#1 AM#1 MDdc MG Ial EL MDﬁ VApc 10m AL#4 F21,2 ProM#2 S22 F22,1 CE#1 Ri#1 S#1 STPg MST TPg F22,2 Cd g S23 F23,1 TSA MI-of TA Pros. Re PI#3 6Va CIT ER#1 V4t CL#4 F23,2 Hyp STG 3b paAc S24 F24,1 Clau PAC#1 Pu c 24d M1-HL VLm 45A 8Ad 9/46d F24,2 D9 S25 F25,1 V1 Ret STSd F25,2 OA S26 F26,1 V3v V3A V6 CITv TEa#3 paAlt VPLc L#1 F26,2 MB SG PO#4 3a F26,3 DP V3 F26,4 Csl S27 F27,1 S1 FD#1 X PFG#1 Opt F27,2 23b TPOr S28 F28,1 1#1 A2 TFM FST IPa VLc V6A F28,2 Insula Pi#1 VIP EI MSTd F28,3 CA1 Pf#2 Ld#2 MT PGa F28,4 V2 EC#2 F28,5 TFL S29 F29,1 Pul#1 SPL PrS SMAr F29,2 Pul.o F4 F29,3 VLo PF#1 F29,4 Ia#2 PL#3 PrCO 2#1 F29,5 Lvl Lv MIP V4 A1 36c F29,6 Bi CM#2 Ldi TAa 46d F29,7 Ig#1 Abpc 8 FEF Iam Iapm PEc#1 Tpt ST1 F29,8 7#1 ABmg MDmc VA MDpc VPL 13M 12r ST2 ST3 TPOc TPPro F29,9 6#1 Bla Cl#2 F6 F3 PEm PECg M9 12m 11l PG#1 F29,10 SI#2 Cd M1 S2 STS Pu r M1-FL IPL Pcn Li F2 7a 31 AITv AITd VAmc 13L 10o continued on next page...

54 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh continued on next page... Shell Fine Shell Brain Regions F29,11 6D 6V F5 PIT 35 TPO 14r 11m 46v 36r F29,12 B#2 L#2 24a 24b Idg PM#3 Iai 7b 45 8A PS F29,13 25 TE 24c 23c 6M LIP ENT TH TF F7 13 12 PGm 36 13a 12l TG F29,14 24 23 MD 32 8B 14 10 9 11 46 12o end of table

55 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh Table S6: Number of connections to be added or deleted in order to affect the core Number of Connec- Number of Extra Con- Brain Regions tions to Core nections to Core 129 100 46 111 82 24 98 69 32 90 61 12o 87 58 9 82 53 12l 80 51 F7 78 49 11 77 48 MD 75 46 13a 73 44 TE PGm 72 43 TH TF 70 41 14 69 40 13 10 64 35 6M LIP 12 63 34 25 61 32 23 36 60 31 24c PM#3 8B 59 30 23c 45 57 28 24b 56 27 M1 ENT 7b TPO 55 26 TG 54 25 6V F2 8A 46v 53 24 L#2 F5 52 23 Iai 35 51 22 M1-FL 6D 50 21 Idg 48 19 36r 47 18 PIT 45 16 S2 14r 44 15 PS 43 14 Cd 6#1 42 13 SI#2 B#2 STS 24a 41 12 F3 PEm PECg 40 11 IPL 39 10 7#1 Pu r Cl#2 Pcn F6 AITd 12m PG#1 38 9 31 AITv VPL 13L 11m 37 8 ABmg PEc#1 TPPro 36 7 Ig#1 Li Ldi 7a ST2 35 6 MIP VAmc 10o M9 34 5 Bla 2#1 MDpc ST3 33 4 Abpc 8 FEF V4 Tpt 13M 11l PF#1 TPOc 32 3 Bi MDmc CM#2 VA PrCO 12r 46d ST1 31 2 Lv PL#3 Pul.o Iam Iapm TAa 30 1 Lvl Ia#2 F4 A1 VLo 36c 29 0 Pul#1 SPL PrS SMAr 28 -1 V2 Pf#2 Ld#2 TFL PGa VLc 27 -2 1#1 EC#2 26 -3 Insula S1 23b X EI IPa 25 -4 CA1 A2 V6A PFG#1 TPOr L#1 24 -5 PAC#1 FD#1 Csl D9 23 -6 Pi#1 MB SG 6Va 3a TFM MT VLm 22 -7 24d STSd CL#4 21 -8 CE#1 Ret M1-HL OA VIP TA Re FST 10m CITv paAlt MSTd TPg 20 -9 Clau ME#1 Pu c MI-of AM#1 MDdc 6Vb Ial ER#1 MDﬁ TEa#3 9/46d 19 -10 Hyp A TSA DP VApc VLps ProM#2 VPLc AL#4 18 -11 STG S#1 CIT Opt 8Ad 17 -12 Pu 3#1 Pros. 29a-c PO#4 3b VPLo paAc 16 -13 30 23a STPg continued on next page...

56 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh ...continued from previous page Number of Connec- Number of Extra Con- Brain Regions tions to Core nections to Core 15 -14 PAC2 Cd g MI-body MG V3 ECL EL EO MST MDmf Cdc Gu 47/12 V6 14 -15 OFC Ri#1 AHA 29 PaS V3v 13 -16 Amyg belt sm IL#2 ABvm VL 4c TPag 12 -17 PR#4 ML AIP ELr 45A 11 -18 V1 Hip Cd t PGop PC#1 20 Clc VPM ProK 10 -19 21 OAa PAa PI#3 COa MDpm Cif V3A TEm 45B TPdgd TPdgv 9 -20 MB#2 Co PFCorb Per#1 LD#1 LIPe LIPi VPI 8 -21 COp V4t CITd PITv 36p 7 -22 belt s AN VN PFop NLOT OFap MTp 10v L9 V3d V4d TPproD 6 -23 CA3 AV MDl PT#2 29d M2-FL Cim PMl 9/46v 5 -24 SN 26 PHC ABd ABv AD#1 MDcd M2-HL 28m Sb Su#2 PMm Cs#2 14O 46vr PITd Pa#2 ELc MSTp 8Ac 4 -25 Bvl PIP#1 C#4 LGN 5 Foot PLd VPS 46dr TPOi 3 -26 MI#1 44 PP DG 10d 2 -27 Sub.Th I#2 ProSt PN 4a 4b 6b-beta CML OFO PIc VAdc SMAc 46f V4v 1 -28 GPe Tha IPro VOT CMA#2 SII-f VP#2 PIl PIm PIp PLvm PLvl 0 -29 Br BG Cx DiE STR CgG#2 FL#2 OC#2 Pl#6 TL#2 Pfc IA#1 VAC PCd#2 PCip TCv GN Ldm PCm STP#2 STSf DI#1 VPP Ts PIl-s PLa#1 9/46 DLc DLr

The third column lists a group of brain regions. All these brain regions have the same number of connections to brain regions in the innermost core. This number is shown in the ﬁrst column. The 122 brain regions in the innermost core are color coded. For the brain regions in the innermost core, the second column shows how many connections can be safely deleted without removing the associated brain region from the innermost core. For the remaining brain regions, the second column shows how many connections need to be added between a brain region and the innermost core for the brain region to become a member of the innermost core. These are shown as negative numbers.

57 www.pnas.org/cgi/doi/10.1073/pnas.1008054107 Modha & Singh