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

TL;DR

This paper introduces Walktrap, an efficient algorithm for detecting communities in large networks using random walk-based similarity measures, outperforming previous methods in quality and speed.

Contribution

The paper presents a novel community detection algorithm, Walktrap, that leverages random walks for similarity measurement, offering improved efficiency and community quality over existing methods.

Findings

Walktrap outperforms previous algorithms in community detection quality.

The algorithm runs efficiently with near-linear time complexity in typical cases.

Extensive tests demonstrate superior performance in large network analysis.

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.