Your Friends Have More Friends Than You Do: Identifying Influential Mobile Users Through Random-Walk Sampling

In this paper, we investigate the problem of identifying influential users in mobile social networks. Influential users are individuals with high centrality in their social-contact graphs. Traditional approaches find these users through centralized algorithms. However, the computational complexity of these algorithms is known to be very high, making them unsuitable for large-scale networks. We propose a lightweight and distributed protocol, iWander, to identify influential users through fixed-length random-walk sampling. We prove that random-walk sampling with O(logn) steps, where n is the number of nodes in a graph, comes quite close to sampling vertices approximately according to their degrees. To the best of our knowledge, we are the first to design a distributed protocol on mobile devices that leverages random walks for identifying influential users, although this technique has been used in other areas. The most attractive feature of iWander is its extremely low control-message overhead, which lends itself well to mobile applications. We evaluate the performance of iWander for two applications, targeted immunization of infectious diseases and target-set selection for information dissemination. Through extensive simulation studies using a real-world mobility trace, we demonstrate that targeted immunization using iWander achieves a comparable performance with a degree-based immunization policy that vaccinates users with a large number of contacts first, while generating only less than 1% of this policy's control messages. We also show that target-set selection based on iWander outperforms the random and degree-based selections for information dissemination in several scenarios.