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.
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. In this article, we innovatively propose a non-backtracking matrix for signed networks , and theoretically derive a detectability threshold and prove the feasibility in community detection. Furthermore, we improve the operator by considering the balanced paths in the network (denoted as balanced non-backtracking operator). Simulation results demonstrate that the balanced non-backtracking matrix-based approach significantly outperforms the adjacency matrix-based and the signed non-backtracking matrix-based algorithm. It shows great potential to detect communities with or without overlap.
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