Effects of Edge Centrality on Random Walks on Graphs

摘要

Random walks are a useful tool to describe and study various dynamical processes on networks. For some particular problems, it is more suitable to formulate them by biased random walks based on the properties of edges, for example, weight and importance. However, in some situations it is not easy to directly observe weight information of a network. In this paper, we show how to extract weight information of edges only from the topological knowledge of a binary network, based on which we develop a framework for biased random walks on the binary network. To this end, we first propose a centrality measure for edges based on line graph. We then present novel biased random walks on a binary network, called edge centrality based random walks (ECBRW), where the walker prefers to jump along edges with high centrality. Furthermore, we develop a series of techniques to derive analytical expressions for relevant quantities of ECBRW, including stationary distribution and hitting times. Finally, we study ECBRW on $m$-ary trees, Barabási–Albert networks and some real networks. We find that the behavior for stationary distribution and hitting times for ECBRW on these networks differs significantly from those for unbiased random walks on corresponding networks.