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Visualization & Graph Drawing 9 October 2012 Martin B. Smith martin@mbs3.org

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Visualization? • Practically any technique using images or diagrams for communication • Not new – cartography is old • Not old – computer graphics are young • Wide applications: architecture, product design, education, communication • A Periodic Table of Visualization Methods

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From social structure, to data, to visualization • People & relationships as data • Mathematical graphs as social networks • Network analysis as applied graph theory

Side note: ‘Storage’ is important • Consider advantages and disadvantages of particular data structures: – Typically breaks down into lists and matrices – Incidence (edge) and Adjacency (vertex) • Rank algorithms by how well they: – Enumerate nodes, test adjacency, etc

Graph theory – Graph drawing • Leonhard Euler, functions, f(x), e, i, Σ, and Seven Bridges of Königsberg, Prussia

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Graph layout • Hierarchical – source to sink • Tree – roots without cycles • Symmetric – create visual symmetry • Orthogonal – min. area & edge crossing • Spectral – eigenvectors of a matrix • Force/MDS – springs and electric charges

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Evaluating graph drawings • Is it fast to compute? Can we parallelize it? • Does the algorithm converge? How quickly? • Does it show obvious symmetries? • Can we adapt it with parameters? • Does it minimize edge crossings? Size? • Does vertex nearness reflect adjacency? • Are sizes, distances and shapes distributed uniformly? • Election 2008 visualization – let’s evaluate

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Force-directed algorithms • Attractive and repulsive forces simulated as a physical system • Forces can be gravity (Newton), springs (Hooke), charged particles (Coulomb), magnetism (Maxwell?) • Advantages: quality, flexibility, interactivity • Disadvantages: can be slow, hurt by local minima or initial conditions

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Two common force-directed algorithms • Fruchterman-Reingold: Nodes as steel rings, edges as springs, electrical repulsive force, step width using a global cooling temperature definition • Kamada-Kawai: Same as above, but instead of a temperature, minimize force equations with some initial node criteria

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What can we do to make graph drawing better for social networks? • Modify the graph, improve data collection • Add constraints to force-directed algorithm • Get better initial conditions, more iterations • Deal with orientations and coordinate systems • 3D -> 2D, or use more interesting forces • Apply multiple layout algorithms • Curved lines and uniform distributions • Come up with better algorithms in general

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EgoNet (egonet.sf.net) • Java, Swing – hosted at SourceForge • Java Universal Network/Graph Framework • Currently defaults to F-R, but places isolates regularly instead of randomly • We’d like to explore other optimizations

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Thank you! • Slides will posted (where?) • Martin Smith – martin@mbs3.org • EgoNet: http://egonet.sf.net/ • JUNG: http://jung.sourceforge.net/

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References • 1. Freeman, L., Visualizing Social Networks. Journal of Social Structure 1(1), Carnegie-Mellon, 2000. • 2. Giuseppe Di Battista, Peter Eades, Roberto Tamassia, Ioannis G. Tollis. Algorithms for Drawing Graphs: an Annotated Bibliography. Computational Geometry: Theory and Applications 4:235-282, 1994. • 3. Tamassia, R. Advances in the Theory and Practice of Graph Drawing. Theoretical Computer Science 217 (2), 1999. • 4. Fruchterman, T. M. J., & Reingold, E. M. Graph Drawing by Force- Directed Placement. Software: Practice and Experience, 21(11), 1991. • 5. Kamada, T. & Kawai, S. (1989). An algorithm for drawing general undirected graphs. Information Processing Letters, 31, 7-15. • 6. Network Workbench Community Wiki at https://nwb.slis.indiana.edu/community/?n=VisualizeData.HomePage