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.