Finding (Short) Paths in Social Networks

Abstract

While several analytic models aim to explain the existence of short paths in social networks such as the web, relatively few address the problem of efficiently finding them, especially in a decentralized manner. Since developing purely decentralized search algorithms in general social-network models appears hard, we relax the notion of decentralized search by allowing the option of storing a small amount of preprocessed information about the network. We show that one can identify a small set of vertices in an undirected social network so that connectivity information of the vertices in this set can be used in conjunction with the local connectivity properties to perform decentralized search and find short paths between vertices. Our results are for random graphs with power law degree distribution generated by a variant of the expected degree model.