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Unformatted text preview: On the Visualization of Social and other Scale-Free Networks Yuntao Jia, Jared Hoberock, Michael Garland, and John C. Hart, Member, IEEE-CS Abstract This paper proposes novel methods for visualizing specifically the large power-law graphs that arise in sociology and the sciences. In such cases a large portion of edges can be shown to be less important and removed while preserving component con- nectedness and other features (e.g. cliques) to more clearly reveal the networks underlying connection pathways. This simplification approach deterministically filters (instead of clustering) the graph to retain important node and edge semantics, and works both auto- matically and interactively. The improved graph filtering and layout is combined with a novel computer graphics anisotropic shading of the dense crisscrossing array of edges to yield a full social network and scale-free graph visualization system. Both quantitative analysis and visual results demonstrate the effectiveness of this approach. Index Terms Scale-free network, edge filtering, betweenness centrality, anisotropic shading 1 INTRODUCTION Social and other scale-free networks are graphs with few nodes of higher degrees and many of lower degrees, such that the number of nodes of degree k follows a power-law distribution . This distri- bution is ubiquitous, natural and commonly found in the relationships studied in sociology, networking, biology and physics. These graphs are rarely planar, and even the best layout methods yield a space-filling jumble of edge crossings for even medium-scale graphs. For example, Fig. 1(a) displays the scale-free network of 1,948 interactions between 1,458 yeast proteins. Such large graphs can be more effectively visualized in a simplified form so long as the simplification preserves the important structures and features of the original. Sec. 2 reviews a variety of graph simplifi- cation methods. Node clustering simplifies graphs by merging neighboring nodes, which when repeated organizes the graph into a hierarchy . Cluster- ing works well on planar graphs. When applied to non-planar graphs, it can actually increase edge density which makes the layout less flex- ible and the display more jumbled with more edge crossings. For ex- ample, the geodesic clustering used for the visualization in Fig. 1(c) increases the edge density from 1.34 to 1.46 edges/node and the effect worsens with the increased clustering of larger graphs. Furthermore, the merged nodes and edges created by node clustering lose their orig- inal semantics. Filtering methods retain edge and node semantics by ensuring the simplified graph is a subgraph of the original. Stochastic filtering ap- proaches statistically sample the graph, scaling well and preserving the expectation of various graph characteristics. But for the visual- ization of scale-free networks where most nodes are of least degree, stochastic filtering can destroy connectivity and other features, as it did in Fig. 1(b).did in Fig....
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- Fall '09