Degree and similarity based search in networks

Decentralized search in networks is an important algorithmic problem in the study of complex networks and graph mining. It has a large number of practical applications, including shortest paths search in social network relationship, web pages search in WWW, querying files in peer-to-peer file sharing networks and so on. In this paper, we present a probabilistic analysis of this search problem that produces a surprisingly simple and effective method. Based on the analysis, we introduce a new decentralized search strategy named Product Search. In this strategy, for every step we forward the message to the neighbor with the minimum product of neighbor's degree and common neighbors' size. We compare this strategy with other common strategies like degree-based search, random walk and breadth-first search. And the results show that the product search outperforms others. We also find that the degree-based search does not do well in high clustering power-law networks, and traditional graph statistical properties such as average path length and skewed degree distribution fail to fully explain the level of search-ability in a network.