Roles in networks

In this paper we offer a topology-driven (‘natural’) definition of subclusters of an undirected graph or network. In addition we find rules for assigning unique roles (from a small set of possible roles) to each node in the network. Our approach is based on the use of a ‘smooth’ index for well-connectedness (eigenvector centrality) which is computed for each node. This index, viewed as a height function, then guides the decomposition of the graph into regions (associated with local peaks of the index), and borders (valleys) between regions. We propose and compare two rules for assigning nodes to regions. We illustrate our approach with simple test graphs, and also by applying it to snapshots of the Gnutella peer-to-peer network from late 2001. This latter analysis suggests that our method implies novel ways of interpreting the notion of well-connectedness for a graph, as these snapshots represent very well connected networks. We argue that our approach is well suited for analyzing computer networks, towards the goal of enhancing their security.