Computing communities in large networks using random walks (long version)

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, and it can be used in an agglomerative algorithm to compute efficiently the community structure of a network. We propose such an algorithm, called Walktrap, 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). Extensive comparison tests show that our algorithm surpasses previously proposed ones concerning the quality of the obtained community structures and that it stands among the best ones concerning the running time.

20 pages, 5 figures, long version

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• Natural Scales in Geographical Patterns
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• Cooperative Game Theory Approaches for Network Partitioning
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• Comparison and Benchmark of Graph Clustering Algorithms
• Community Detection Clustering via Gumbel Softmax
• Weighted Graph Nodes Clustering via Gumbel Softmax
• Simplification of networks via conservation of path diversity and minimisation of the search information
• Revisiting Causality Inference in Memory-less Transition Networks