Before revision:   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.
After revision:  Furthermore, we improve the operator by considering the balanced paths in the network (denoted as balanced non-backtracking operator). 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.