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XYZ Decompositions of Graphs Dagstuhl Seminar 08191 XYZ decom- positions V. Batagelj XYZ decompositions of graphs Dagstuhl Seminar 08191 Motivation XYZ decom- Vladimir Batagelj positions Results University of Ljubljana, FMF, Dept. of Mathematics; and References IMFM Ljubljana, Dept. of Theoretical Computer Science joint work with Franz J. Brandenburg, Walter Didimo, Giuseppe Liotta, Maurizio Patrignani 23rd Leoben-Ljubljana Graph Theory Seminar Ljubljana, 14-15. November 2008 V. Batagelj XYZ decompositions Outline XYZ decom- positions V. Batagelj Dagstuhl Seminar 08191 Motivation 1 XYZ decom- Dagstuhl Seminar 08191 positions 2 Motivation Results 3 XYZ decompositions References 4 Results 5 References V. Batagelj XYZ decompositions Dagstuhl Seminar 08191 XYZ decom- positions V. Batagelj Dagstuhl Seminar 08191 Motivation XYZ decom- positions Results References Dagstuhl Seminar 08191: Graph Drawing with Applications to Bioinformatics and Social Sciences. Dagstuhl, May 4-9, 2008 V. Batagelj XYZ decompositions Motivation XYZ decom- positions For dense graphs the matrix representation is better [3]. Pajek - shadow [0.00,1.00] V. Batagelj uki fra wge jap net ita usa bel lux car swe kod den swi can nor par spa irn Dagstuhl yem mat irq pak ire nau aut bol hun Seminar 08191 lib hai isr nic sau alb kuw aus gua mon fin por zai hon bra arg pol syr cze kmr usr Motivation tri ege yug sri ind cha saf gre tur sie egy bul rum uru tai rum syr XYZ decom- leb upv cyp vnr ice arg tun gab cub liy positions pol mor usr lux alg spanor nig isr mli uga ins bul liy ken mex usa eth brm pan net tha cze fra jor sud gre jap sri eth gha Results can ita kor ind vnr col bur ege chd phi swe guinep por nze nze bra vnd tha tai uki tur mla maa ins sau pak wge els saf uga con mex den col References chi cha uru yug bel per chi swi ven ecu phi lib dom dom irn mor kor zai egy jam cyp tri aus pan aut sen alg ivo cam els ire cos lebhun gua irq hon fin per nic ven nig car kuw gha afg chd rwa nau ice sen tog dah cub ecu nir som gab sie sud con mla brm hai tun ivo gui mat bol cos par cam ken jam maa nir yem kod lao mon nep bur rwa tog vnd som afg mli dah upv alb kmr lao jor uki fra wge jap net ita usa bel lux swe den swi can nor spa irn irq pak ire aut hun isr sau kuw aus fin por bra arg pol cze usr ege yug ind cha gre tur egy bul rum syr leb cyp ice tun cub liy mor alg nig uga ken eth brm tha sud sri gha kor vnr phi nze tai mla ins saf mex col uru per chi ven ecu lib dom zai jam tri pan sen ivo els cos gua hon nic car chd nau tog dah nir gab sie con hai gui mat bol par cam maa yem kod lao mon nep bur rwa vnd som afg mli upv alb kmr jor Snyder and Kick World Trade data (SaKtrade.paj; 118 vertices, 515 arcs, 2116 edges) [18]. V. Batagelj XYZ decompositions Motivation XYZ decom- positions Abello and van Ham (Matrix Zoom, ASK-GraphView) [1] and V. Batagelj Henry and Fekete (MatrixExplorer, NodeTrix) [9, 10] developed systems for mixed representation of large networks. Dagstuhl Seminar 08191 Motivation XYZ decom- positions Results References (a) Clustered node-link (b) NodeTrix (c) Node duplications V. Batagelj XYZ decompositions Figure 7.1: NodeTrix and duplications 7.1 Research problem As previously explained in section 2.2, social networks can vary a lot in structure: from sparse graphs exhibiting a tree structure to very dense ones presenting a table-like structure. Select- ing the most suited representation is strongly correlated to the network density. For example, node-link diagrams are particularly effective for very sparse networks while matrix representa- tion clearly outperform them for very dense networks [GFC05]. The difficulty is to identify the density threshold beyond which matrices are more suited than node-link diagrams. This choice is especially ambiguous for small-world networks, a very common category of social networks. The particularity of small-world networks is their global sparse structure with dense local parts. The major difficulty faced when representing these network is to show first how members of communities are connected (intra-community connectivity), then how communities are connected (inter-community connectivity) and finally who the central actors are. Thus, in this chapter, we attempt to solve the following question: ®How can we design a representation for small-world networks? i.e., improving intra-community and inter-community connectivity readability as well as highlighting central actors? The second part of this chapter is dedicated to the problem of ambiguous clustering. When an actor is connected to two or more communities, there are three solutions: placing the actor in one or the other, extracting it and placing it between them or generating overlapping commu- nities. While extracting the actor and producing overlapping communities dramatically decrease the representation readability, choosing one or the other community to place the central actor also raises problems as it changes the visual representation, which is potentially misleading. Thus our research question is: ®How can we solve the problem of ambiguous clustering without degrading the representation readability or misleading the user? To solve these problems, we present the NodeTrix [HFM07] representation (Figure 7.1b), merging node-link diagrams and matrices to visualize social networks as well as the technique of node duplication [HBF08] (Figure 7.1c) to solve the ambiguous clustering problem. NodeTrix 149 Supporting the exploration of matrices One weakness of the matrix representation, when ex- ploring a network, is the tedious work required to perform path-related tasks. For example, finding how two communities are connected is tedious as it requires going back and forth alternately read- ing rows and columns. Moreover, if communities are far apart in the matrix, this task requires a scan of the full length of matrix rows or columns, and connections in a large matrix may lie outside the viewport. Obviously, the task is worse when dealing with three matrices as the user needs to check for intersections of rows and columns in each of the three communities. We noticed in a participatory-design session reported in [HF06a] that social network analysts also use the matrix representation for some of their analyses. To help perform community analysis and provide support for path-related tasks in general, we provide users with a couple of interaction techniques that work across separate matrix-NodeTrix windows that might be arranged in a dual- viewport or split-screen fashion. These techniques are still based on drag-and-drop, however this time, the user drags a group of elements from one window to another one. From Matrix to NodeTrix The interaction is made of two steps: first, the user selects a group of nodes in the window of the pure matrix visualization and then drags this group to the MotivationNodeTrix window (Figure 7.5). To select the group of nodes, we provide lasso selection directly on the pure matrix representation. Alternatively, the selection can be done on an axis (rows and columns). When a group of cells is selected, the corresponding set of vertices transferred is the XYZ decom- union of the edges’ source vertices and sink vertices. Dropping the selected group inside the positions NodeTrix window performs the addition of an aggregated node to the NodeTrix visualization. The V. Batagelj group is then displayed as a matrix. Selecting and dropping a second group allows the user to see how these groups are connected to each other visualizing the result with links. The process can Dagstuhl continue to visualize connections between several communities. Seminar 08191 Motivation XYZ decom- positions Results References (a) From matrix to NodeTrix (b) Inter-community connectivity appears Figure 7.5: Dragging communities from standard matrix to NodeTrix helps analyzing how they are connected. (a) A community has already been dragged into NodeTrix (rows are colored in white in the matrix to show they are already copied). User is transferring another community (rows selected in red in the matrix), the cursor shows that he can drop the selection into NodeTrix. (b) Three communities have beenV. dragged Batagelj into NodeTrix,XYZ decompositions inter-community relations can be studied. Motivation XYZ decom- positions V. Batagelj Dagstuhl Seminar 08191 MotivationNodeTrix 155 XYZ decom- positions Results References (a) Compact NodeTrix V. Batagelj XYZ decompositions (b) Detailed NodeTrix Figure 7.11: Two NodeTrix representations of the information visualization field. The top one presents a compact version, which aims at presenting communities and their connectivity patterns (intra-community and inter-community). The second representation shows all details of the exact same dataset, which can be used for exploration. Colors on axes of matrices represent the number of citations of each author. Color intensity within the matrices represents the strength of each collaboration. Motivation XYZ decom- positions V. Batagelj UIST Coauthorship Network 20 Years of Collaboration Sidner Stahovich Rich Kara Newfield Sethi Hindmarsh Benford Fraser Heath Goldberg J. Rich Dahlquist Partridge Foreman Borriello Kara Veiseh Latulipe Hardock Sidner McMahon Kaplan Wittenburg Tapia Cain Clarke Heinrichs Stahovich Esenther MacKay D. McKay Lanning Thevenin Stanton Lecoanet Miyachi Harada Blackwell Newfield York Lemort Chatty Mertz Vinot Ward Churchill Sire Helfman Yamada Sethi Denoue Murphy Nelson Shingu Kurtenbach Fitzmaurice Fraser Almeida Burtnyk Meier Buxton Benford Cain Tsang Pieké Khan Herranz Latulipe Oscarsson Danielsson Nordgard Holmquist Hindmarsh Redstrom Dahlquist McKay Karlgren Franzén Raeder Bolt Clarke Heinrichs Hauge Bretan Lecoanet Blackwell Bjork Heath York Veiseh Stonebraker Kaplan Esenther Sire Weiser Dagstuhl Yamada Woodruff Ward McMahon Foreman schraefel Harada Takashima Mertz Kitamura Murphy Smith MacKay D.
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