In this paper, we tackle the problem of topology inference in wireless mesh networks and present a novel approach to reconstructing the logical network topology. Our approach is based on the social fingerprint, a short bit pattern computed for each node to characterize the link status of the local neighborhood of the node. To conserve the communication resource, social fingerprints are piggybacked to the gateway with a small probability. Based on the information embedded in the social fingerprints, the gateway first estimates the set of parameters defining a Hidden Markov Model (HMM) that models the logical network topology, then infers the evolutions of the local and global network topologies. We have conducted extensive simulation to verify the performance of our approach in terms of "completeness" and "accuracy". The results indicate that our approach is very effective in topology inference.