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Community detection or clustering is a crucial task for understanding thestructure of complex systems. In some networks, nodes are permitted to belinked by either "positive" or "negative" edges; such networks are calledsigned networks. Discovering communities in signed networks is more challengingthan that in unsigned networks. In this study, we innovatively develop anon-backtracking matrix of signed networks, theoretically derive adetectability threshold for this matrix, and demonstrate the feasibility ofusing the matrix for community detection. We further improve the developedmatrix by considering the balanced paths in the network (referred to as abalanced non-backtracking matrix). Simulation results demonstrate that thealgorithm based on the balanced nonbacktracking matrix significantlyoutperforms those based on the adjacency matrix and the signed non-backtrackingmatrix. The proposed (improved) matrix shows great potential for detectingcommunities with or without overlap.

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