Efficient algorithm based on non-backtracking matrix for community detection in signed networks

TL;DR

This paper introduces a novel non-backtracking matrix approach for community detection in signed networks, deriving a detectability threshold and demonstrating improved performance over traditional methods through simulations.

Contribution

It develops a new non-backtracking matrix for signed networks, derives its detectability threshold, and enhances community detection by considering balanced paths.

Findings

The balanced non-backtracking matrix outperforms adjacency-based methods.

The approach effectively detects communities with or without overlap.

Simulation results validate the method's superiority.

Abstract

Community detection or clustering is a crucial task for understanding the structure of complex systems. In some networks, nodes are permitted to be linked by either "positive" or "negative" edges; such networks are called signed networks. Discovering communities in signed networks is more challenging than that in unsigned networks. In this study, we innovatively develop a non-backtracking matrix of signed networks, theoretically derive a detectability threshold for this matrix, and demonstrate the feasibility of using the matrix for community detection. We further improve the developed matrix by considering the balanced paths in the network (referred to as a balanced non-backtracking matrix). Simulation results demonstrate that the algorithm based on the balanced nonbacktracking matrix significantly outperforms those based on the adjacency matrix and the signed non-backtracking matrix. The proposed (improved) matrix shows great potential for detecting communities with or without overlap.