Determining and Understanding Dynamically Important Differences between Complex Networks Using Reliability-Induced Structural Motifs

We demonstrate how to compare networks using a novel family of measures of an edge's contribution to particular aspects of diffusion dynamics on a network. These centrality measures are based on membership in structural motifs that determine the network's reliability, as introduced by Moore and Shannon in 1956. Moore:56 The measures are analogous to between ness, but are more directly related to specific dynamical phenomena. They can be estimated efficiently in a distributed, scalable way with readily controlled precision. We illustrate how these measures can be used to understand which differences between two networks over the same set of vertices are most important, and exactly how those differences affect the dynamics. We focus here on phenomena of interest in network epidemiology, but the methods can easily be generalized to other diffusive processes on a network.