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SignedLouvain: Louvain for signed networks

John N. Pougué-Biyong, Renaud Lambiotte

TL;DR

SignedLouvain addresses community detection in signed networks by maximizing a signed modularity $Q$. It introduces a two-layer multiplex framework with hop-bounded moves defined by $d_{+}$ and $d_{-}$ to guide node reassignment. Empirical results on synthetic SBMs and real networks show that SignedLouvain matches or surpasses the accuracy of RelaxedLouvain while remaining substantially faster, with default $d_{+}=1$, $d_{-}=2$ offering a favorable trade-off. The authors provide public data and code to enable reproducibility and further exploration.

Abstract

In this article, we consider the problem of community detection in signed networks. We propose SignedLouvain, an adaptation of the Louvain method to maximise signed modularity, efficiently taking advantage of the structure induced by signed relations. We begin by identifying the inherent limitations of applying the standard Louvain algorithm to signed networks, before introducing a novel variant specifically engineered to overcome these challenges. Through extensive experiments on real-world datasets, we demonstrate that the proposed method not only maintains the speed and scalability of its predecessor but also significantly enhances accuracy in detecting communities within signed networks.

SignedLouvain: Louvain for signed networks

TL;DR

SignedLouvain addresses community detection in signed networks by maximizing a signed modularity . It introduces a two-layer multiplex framework with hop-bounded moves defined by and to guide node reassignment. Empirical results on synthetic SBMs and real networks show that SignedLouvain matches or surpasses the accuracy of RelaxedLouvain while remaining substantially faster, with default , offering a favorable trade-off. The authors provide public data and code to enable reproducibility and further exploration.

Abstract

In this article, we consider the problem of community detection in signed networks. We propose SignedLouvain, an adaptation of the Louvain method to maximise signed modularity, efficiently taking advantage of the structure induced by signed relations. We begin by identifying the inherent limitations of applying the standard Louvain algorithm to signed networks, before introducing a novel variant specifically engineered to overcome these challenges. Through extensive experiments on real-world datasets, we demonstrate that the proposed method not only maintains the speed and scalability of its predecessor but also significantly enhances accuracy in detecting communities within signed networks.
Paper Structure (10 sections, 4 equations, 3 figures, 1 table)

This paper contains 10 sections, 4 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Louvain on signed networks
  3. Approach
  4. Caveats
  5. SignedLouvain: Louvain for signed networks
  6. Method
  7. Experiments
  8. Discussion
  9. Acknowledgements
  10. Data and code availability

Figures (3)

  • Figure 1: Performance of Louvain v RelaxedLouvain v Signed Louvain on a Signed Stochastic Block Model. The colour indicates the NMI of the final partition with the one used to build the SSBM. As can be seen, the quality of the original Louvain remains low in situations when the density of negative edges between communities is large.
  • Figure 2: Example of graph where RelaxedLouvain may produce inconsistent clusters, for instance $\{0, 5, 6\}$, due to to its lack of locality during the optimisation.
  • Figure 3: Modularity vs Duration. $L$ stands for Louvain, $SL_d$ for default SignedLouvain, $SL_e$ for extended SignedLouvain, and $RL$ for RelaxedLouvain.