An improvement on the Louvain algorithm using random walks

Duy Hieu Do () and Thi Ha Duong Phan ()
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Duy Hieu Do: Vietnam Academy of Science and Technology
Thi Ha Duong Phan: Vietnam Academy of Science and Technology

Journal of Combinatorial Optimization, 2025, vol. 50, issue 2, No 2, 26 pages

Abstract: Abstract We present improvements to famous algorithms for community detection, namely Newman’s spectral method algorithm and the Louvain algorithm. The Newman algorithm begins by treating the original graph as a single cluster, then repeats the process to split each cluster into two, based on the signs of the eigenvector corresponding to the second-largest eigenvalue. Our improvement involves replacing the time-consuming computation of eigenvalues with a random walk during the splitting process. The Louvain algorithm iteratively performs the following steps until no increase in modularity can be achieved anymore: each step consists of two phases–phase 1 for partitioning the graph into clusters, and phase 2 for constructing a new graph where each vertex represents one cluster obtained from phase 1. We propose an improvement to this algorithm by adding our random walk algorithm as an additional phase for refining clusters obtained from phase 1. It maintains a complexity comparable to the Louvain algorithm while exhibiting superior efficiency. To validate the robustness and effectiveness of our proposed algorithms, we conducted experiments using randomly generated graphs and real-world data.

Keywords: Community detection; Random walk; Louvain algorithm; Newman’s spectral method (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-025-01337-9

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