A Two-Parameter Method to Characterize the Network Reliability for Diffusive Processes

Abstract

We introduce a new method to characterize the network reliability polynomial of graphs – and hence the graph itself – using only a few parameters. Exact evaluation of the reliability polynomial is almost impossible for large graphs; estimating the polynomial’s coefficients is feasible but requires significant computation. Furthermore, the information required to specify the polynomial scales with the size of the graph. Thus, we aim to develop a way to characterize the polynomial well with as few parameters as possible. We show that the error function provides a two-parameter family of functions that can closely reproduce reliability polynomials of both random graphs and synthetic social networks. These parameter values can be used as statistics for characterizing the structure of entire networks in ways that are sensitive to dynamical properties of interest.