Visual Clustering of Graphs with Nonuniform Degrees

We discuss several criteria for clustering graphs, and identify two cri- teria which are not biased towards certain cluster sizes: the node-normalized cut (also called cut ratio) and the edge-normalized cut. We present two energy mod- els whose minimum energy drawings reveal clusters with respect to these criteria. The energy model that corresponds to the edge-normalized cut differs from the other energy model in that it is also useful for graphs with very nonuniform node degrees. We show that its drawings provide insights into the structure of an airline routing graph, a citation graph, a social network, and a thesaurus graph.

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