A nearly-sublinear method for approximating a column of the matrix exponential for matrices from large, sparse networks

Abstract

We consider random-walk transition matrices from large social and information networks. For these matrices, we describe and evaluate a fast method to estimate one column of the matrix exponential. Our method runs in sublinear time on networks where the maximum degree grows doubly logarithmic with respect to the number of nodes. For collaboration networks with over 5 million edges, we find it runs in less than a second on a standard desktop machine. © 2013 Springer International Publishing.