Computing Communities in Large Networks Using Random Walks

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Abstract

Dense subgraphs of sparse graphs (communities), which appear in most real-world complex networks, play an important role in many contexts. Computing them however is generally expensive. We propose here a measure of similarities between vertices based on random walks which has several important advantages: it captures well the community structure in a network, it can be computed efficiently, it works at various scales, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm which runs in time O(mn 2) and space O(n 2) in the worst case, and in time O(n 2log n) and space O(n 2) in most real-world cases (n and m are respectively the number of vertices and edges in the input graph).