Non-backtracking Operator for Community Detection in Signed Networks

Community detection or clustering is crucial for understanding the structure of complex systems. In some networks, nodes are allowed to be linked by either 'positive' or 'negative' edges. Such networks are called signed networks. Discovering communities in signed networks is more challenging. Inspired by the structural balance theory, in this article, we innovatively propose a non-backtracking operator for signed networks. Besides, we theoretically derive a detectability threshold and prove the feasibility of the non-backtracking operator in community detection. Simulation results demonstrate that the non-backtracking matrix-based approach significantly outperforms the adjacency matrix-based algorithm, and shows great potential to detect communities with or without overlap.