  Community detection is of fundamental significance for understanding the
topology characters and the spreading dynamics on complex networks. While
random walk is widely used and is proven effective in many community detection
algorithms, there still exists two major defects: (i) the maximal length of
random walk is too large to distinguish the clustering information if using the
average step of all possible random walks; (ii) the useful community
information at all other step lengths are missed if using a pre-assigned
maximal length. In this paper, we propose a novel community detection method
based on the first passage probabilities (FPPM), equipped with a new similarity
measure that incorporates the complete structural information within the
maximal step length. Here the diameter of the network is chosen as an
appropriate boundary of random walks which is adaptive to different networks.
Then we use the hierarchical clustering to group the vertices into communities
and further select the best division through the corresponding modularity
values. Finally, a post-processing strategy is designed to integrate the
unreasonable small communities, which significantly improves the accuracy of
community division. Surprisingly, the numerical simulations show that FPPM
performs best compared to several classic algorithms on both synthetic
benchmarks and real-world networks, which reveals the universality and
effectiveness of our method.
