Community Detection and Classification in Hierarchical Stochastic Blockmodels

We propose a robust, scalable, integrated methodology for community detection\nand community comparison in graphs. In our procedure, we first embed a graph\ninto an appropriate Euclidean space to obtain a low-dimensional representation,\nand then cluster the vertices into communities. We next employ nonparametric\ngraph inference techniques to identify structural similarity among these\ncommunities. These two steps are then applied recursively on the communities,\nallowing us to detect more fine-grained structure. We describe a hierarchical\nstochastic blockmodel---namely, a stochastic blockmodel with a natural\nhierarchical structure---and establish conditions under which our algorithm\nyields consistent estimates of model parameters and motifs, which we define to\nbe stochastically similar groups of subgraphs. Finally, we demonstrate the\neffectiveness of our algorithm in both simulated and real data. Specifically,\nwe address the problem of locating similar subcommunities in a partially\nreconstructed Drosophila connectome and in the social network Friendster.\n

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