Community detection based on first passage probabilities

Community detection is of fundamental significance for understanding topology characters and spreading dynamics on complex networks. While random walk is widely used in previous algorithms, there still exist two major defects: (i) the maximal length of random walk in some methods is too large to distinguish different communities; (ii) the useful community information at all other step lengths are missed if using a pre-assigned maximal length. Here we propose a novel community detection algorithm named as First Passage Probability Method (FPPM), equipped with a new similarity measure that incorporates the complete structural information within the maximal step length. The diameter of the network is chosen as an appropriate boundary of random walks, which is adaptive to different networks. Numerical simulations show that FPPM performs best compared to several classic algorithms on both synthetic benchmarks and real-world networks, especially those with weak community structures.