Social Networks

Social networks provide a rich source of graph drawing problems, because they appear in an incredibly wide variety of forms and contexts. After sketching the scope of social network analysis, we establish some general principles for social network visualization before finally reviewing applications of, and challenges for, graph drawing methods in this area. Other accounts more generally relating to social network visualization are given, e.g., in [Klo81, BKR + 99a, Fre00, Fre05, BKR06]

Origin of Biomolecular Networks

Biomolecular networks have already found great utility in characterizing complex biological systems arising from pair-wise interactions amongst biomolecules. Here, we review how graph theoretical approaches can be applied not only for a better understanding of various proximate (mechanistic) relations, but also, ultimate (evolutionary) structures encoded in such networks. A central question deals with the evolutionary dynamics by which different topologies of biomolecular networks might have evolved, as well as the biological principles that can be hypothesized from a deeper understanding of the induced network dynamics. We emphasize the role of gene duplication in terms of signaling game theory, whereby sender and receiver gene players accrue benefit from gene duplication, leading to a preferential attachment mode of network growth. Information asymmetry between sender and receiver genes is hypothesized as a key driver of the resulting network topology. The study of the resulting dynamics suggests many mathematical/computational problems, the majority of which are intractable but yield to efficient approximation algorithms, when studied through an algebraic graph theoretic lens

Drawing power law graphs using a local/global decomposition

Abstract. It has been noted that many realistic graphs have a power law degree distribution and exhibit the small-world phenomenon. We present drawing methods influenced by recent developments in the modeling of such graphs. Our main approach is to partition the edge set of a graph into “local ” edges and “global ” edges and to use a standard drawing method that allows us to give added importance to local edges. We show that our drawing method works well for graphs that contain underlying geometric graphs augmented with random edges, and we demonstrate the method on a few examples. We define edges to be local or global depending on the size of the maximum short flow between the edge’s endpoints. Here, a short flow, or alternatively an ℓ-short flow, is one composed of paths whose length is at most some constant ℓ. We present fast approximation algorithms for the maximum short flow problem and for testing whether a short flow of a certain size exists between given vertices. Using these algorithms, we give an algorithm for computing approximate local subgraphs of a given graph. The drawing algorithm we present can be applied to general graphs, but it is particularly well suited for small-world networks with power law degree distribution. Key Words

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Drawing power law graphs using a local/global decomposition. (English summary

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Drawing power law graphs using a local/global decomposition. (English summary