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Graphs, Trees and Networks Graphs, Trees and Networks IAT 355 Is this a network? IAT 355 | Graphs, Networks and Trees Is this a network? IAT 355 | Graphs, Networks and Trees Is this a network? IAT 355 | Graphs, Networks and Trees www.perceptualedge.com Is this a network? • Introduction • Definition • Problem statement • Background • Related concepts in perception • Related concepts in visualization • Approach • Using colour • Colour mapping for meaning • Study • Results • Conclusion and future work IAT 355 | Graphs, Networks and Trees Is this a network? https://mkokos.wordpress.com/fourth-semester/personal-network-infographic/ IAT 355 | Graphs, Networks and Trees We live in a connected world • Online Social networks: Facebook, Twitter ~ people connected online • Information networks: WWW ~ web pages connected through hyperlinks • Computer networks: The internet ~ computers and routers connected through wired/wireless connections • What is a network? “any collection of objects in which some pairs of these objects are connected by links” [Easley and Kleinberg, 2011] IAT 355 | Graphs, Networks and Trees Visualizing Relations Why relations? Isn’t all data inherently relational? • Visualising data: seeing the patterns between the data values and attributes that emerge and associate or disassociate in some way • Visualising relations: when how one datum relates to another is an element in itself • We want to see the overall structure of the data set • Patterns emerge from structure as well as from values/ attributes IAT 355 | Graphs, Networks and Trees Common Applications • Process Visualization (e.g., • Concept maps Visio) • Ontologies • Dependency Graphs • Simulation and Modeling • Biological Interactions • Probability maps (Genes, Proteins) • Computer Networks • Social Networks IAT 355 | Graphs, Networks and Trees Process flow diagrams IAT 355 | Graphs, Networks and Trees Dependency graphs IAT 355 | Graphs, Networks and Trees Gene networks IAT 355 | Graphs, Networks and Trees Computer networks IAT 355 | Graphs, Networks and Trees Internet • What does the Internet look like? • Email paths Nature, 406, 353-354(27 July 2000) IAT 355 | Graphs, Networks and Trees Social networks IAT 355 | Graphs, Networks and Trees Concept maps IAT 355 | Graphs, Networks and Trees Ontologies IAT 355 | Graphs, Networks and Trees Simulation graphs IAT 355 | Graphs, Networks and Trees Probability maps • Bayesian network IAT 355 | Graphs, Networks and Trees • Several ways to represent relations • Choice depends on relation, task and scale T. Munzner, Visualization Analysis and Design. IAT 355 | Graphs, Networks and Trees When is Graph Visualization Applicable? • Ask the question: is there an inherent relation among the data elements to be visualized? • If YES – then the data can be represented by nodes of a graph, with edges representing the relations. • If NO – then the data elements are “unstructured” and goal is to use visualization to analyze and discover relationships among data. Source: Herman, Graph Visualization and Navigation in Information Visualization: a Survey IAT 355 | Graphs, Networks and Trees Graphs as Network Models • Graphs are only ONE way to represent networks • Most powerful • Most popular • Graphs are well suited for topology-related problems • Distance through the network (hops), propagation, clusters defined by connectivity { arc , link , edge } { node , vertex } Source: L. Adamic SNA class @coursera Network Visualization, QMSS @ Columbia @denisparra IAT 355 | Graphs, Networks and Trees Graphs, Networks and Trees • A graph (network) is a set of objects connected together • Objects == nodes, vertices • Connections == links, edges • • A path is the/a set of connections from node a to node b • Topology is a schematic description of the arrangement of a graph/network, including nodes and links IAT 355 | Graphs, Networks and Trees What kinds of relations? • Associative (IS-A) • A is like B in some way • Ordinal/Sequential • A > B, precedes B, in some way • Time • Hierarchy • Influence • Causal • dependency IAT 355 | Graphs, Networks and Trees Graphs: the problem • YUK …… IAT 355 | Graphs, Networks and Trees • Tree with 3238 nodes 3 different views of the same graph, made using Tulip IAT 355 | Graphs, Networks and Trees Graph Terminology A-C Hops 2 C-A Hops 0 • Graphs can have cycles A B C • Edges can be directed or undirected • Degree of a vertex = # connected nodes A • In-degree and out-degree for directed In-degree 2 graphs Out-degree 1 • Graph edges can have values (weights) • Nominal (N), ordinal (O), quantitative (Q) IAT 355 | Graphs, Networks and Trees What’s important here? IAT 355 | Graphs, Networks and Trees What’s important here? IAT 355 | Graphs, Networks and Trees Or here? Community structure concepts • Cliques are subgraphs in which every node is connected to every other node in the clique. • Cluster coefficient is a measure of how close a group is to being a clique. IAT 355 | Graphs, Networks and Trees Graph tasks 1: topology A-C Hops 2 • Finding all possible paths C-A Hops 0 A B C • Shortest path • Distance/proximity: A • All adjacent nodes <n> hops away In-degree 2 • Degree (how many nodes connect in or out) Out-degree 1 • Flow through the network (directional) • Finding bridges that connect clusters or components IAT 355 | Graphs, Networks and Trees Undirected Directed multimode Weighted and (Facebook (Twitter (Amazon user- (Facebook more friendships) following) product) likes) …. 9 3 IAT 355 | Graphs, Networks and Trees Network Analysis measures Node-level metrics Graph-level metrics • Centrality • Size • (In/Out) Degree • Diameter (longest path) • Betweenness • Average path length • Closeness • Average [node metric] • Eigenvector • Clustering coefficient • These are only a few representative measures • http://www.slideshare.net/gcheliotis/social-network-analysis-3273045 IAT 355 | Graphs, Networks and Trees Interpretation of measures Interpretation in Social Networks Degree How many people can this person reach directly? Betweenness How likely is this person to be the most direct route between two people in the network? Source: http://www.slideshare.net/gcheliotis/social-network-analysis-3273045 slide 24 IAT 355 | Graphs, Networks and Trees Interpretation of measures Interpretation in Social Networks Closeness How fast can this person reach everyone in the network? Eigenvector How well is this person connected to other well-connected people? Source: http://www.slideshare.net/gcheliotis/social-network-analysis-3273045 IAT 355 | Graphs, Networks and Trees Two more concepts… • Total possible number of edges in a network • #edges = n * (n -1 ) /2 (undirected network) • #edges = n * (n -1 ) (directed network) • (Shortest) Path: the shortest sequence of edges to be followed to reach a node B from a node A in a network. Which is the length of the shortest path between Rafa Nadal and Sharonpova? IAT 355 | Graphs, Networks and Trees Using these concepts in network analysis • compare these 2 movie networks (characters’ interactions) Source: http://moviegalaxies.com Forrest Gump (1994) Traffic (2000) IAT 355 | Graphs, Networks and Trees Network metrics: Abbie Hoffman Forrest Gump (1994) • Size: 94/271 • Density: 0.06 • Diameter: 4 • Clustering coefficient: 0.8 • Avg. Path Length: 1.99 Node metrics: Forrest • Degree: 89 • Betweetnness: 3453.8 Abbie Hoffman • Degree: 6 • Betweenness: 0 http://moviegalaxies.com/movies/316-Forrest-Gump IAT 355 | Graphs, Networks and Trees Traffic (2000) Network metrics: • Size: 68 • Density: 0.04 • Diameter: 7 • Clustering coefficient: 0.55 • Avg. Path Length: 3.54 Node metrics: Robert • Degree: 24 * Francisco: is a bridge (structural holes) • Betweenness: 1437.7 Francisco • Degree: 5 • Betweenness: 1031 http://moviegalaxies.com/movies/837-Traffic IAT 355 | Graphs, Networks and Trees Design Choices 1 • Depends on key connectivity relationships to be prioritized IAT 355 | Graphs, Networks and Trees Node-link diagrams Most common idiom for network and tree data Blog.visual.ly SAS Constellation Tool IAT 355 | Graphs, Networks and Trees Node-link diagrams Most common idiom for network and tree data Rectilinear Radial B. Harvey & M. Wright. Simply Scheme, Introducing IBM Java Vis blog Computer Science IAT 355 | Graphs, Networks and Trees Vertex/Node choices • Colour • Size • Label • Form/Shape • Location/Layout IAT 355 | Graphs, Networks and Trees Edge options • Colour • Thickness • Label • Form • Polyline, straight, orthogonal, grid, curved, planar up/down … IAT 355 | Graphs, Networks and Trees Aesthetic constraints • Minimize link crossings • Often unsuitable for • Minimize link lengths interactive visualisation • Area – minimize towards • Approximation algorithms efficiency very complex • Unless you only need to • Minimize link bends compute layout once • uniform edge lengths – • Precompute layout, or minimise variances compute once at the • Minimize lomgest edge beginning of an application then support interaction • Mathematically difficult to do everything ! IAT 355 | Graphs, Networks and Trees Which is most important? • Various studies • BUT • Purchase, Graph Drawing ’97 • A recent study (Xu et al 2012) • Ware et al, Info Vis 1(2) found edge crossings less • Ghoniem et al, Info Vis 4(2) important than path distance • van Ham & Rogowitz, TVCG and smoothness ’08 • Curved lines may be preferred • Results mixed: Edge but performance is better with crossings do seem important straight .. IAT 355 | Graphs, Networks and Trees Aesthetics are not yet defined fully [Xu et al. 2012] • Lombardi layout a reasonable approach, •
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