A connectivity rating for vertices in networks

Abstract

We compute the influence of a vertex on the connectivity structure of a directed network by using Shapley value theory. In general, the computation of such ratings is highly inefficient. We show how the computation can be managed for many practically interesting instances by a decomposition of large networks into smaller parts. For undirected networks, we introduce an algorithm that computes all vertex ratings in linear time, if the graph is cycle composed or chordal. © 2006 International Federation for Information Processing.