A semi-parametric statistical test to compare complex networks

Abstract

The modelling of real-world data as complex networks is ubiquitous in several scientific fields, for example, in molecular biology, we study gene regulatory networks and protein–protein interaction (PPI)_networks; in neuroscience, we study functional brain networks; and in social science, we analyse social networks. In contrast to theoretical graphs, real-world networks are better modelled as realizations of a random process. Therefore, analyses using methods based on deterministic graphs may be inappropriate. For example, verifying the isomorphism between two graphs is of limited use to decide whether two (or more) real-world networks are generated from the same random process. To overcome this problem, in this article, we introduce a semi-parametric approach similar to the analysis of variance to test the equality of generative models of two or more complex networks. We measure the performance of the proposed statistic using Monte Carlo simulations and illustrate its usefulness by comparing PPI networks of six enteric pathogens.