Evaluating the Natural Variability in Generative Models for Complex Networks

Abstract

Complex networks are used to represent real-world systems using sets of nodes and edges that represent elements and their interactions, respectively. A principled approach to understand these network structures (and the processes that give rise to them) is to formulate generative models and infer their parameters from given data. Ideally, a generative model should be able to synthesize networks that belong to the same population as the observed data, but most models are not designed to accomplish this task. Due to the scarcity of data in the form of populations of networks, generative models are typically formulated to learn parameters from a single network observation, hence ignoring the natural variability of network populations. In this paper, we evaluate four generative models with respect to their ability to synthesize networks that belong to the same population as the observed network. Our empirical analysis quantifying the ability of network models to replicate characteristics of a population of networks highlights the need for rethinking the way we evaluate the goodness of fit of new and existing network models.