Network Onion Divergence: Network representation and comparison using nested configuration models with fixed connectivity, correlation and centrality patterns (2204.08444v1)

Abstract: Random networks, constrained to reproduce specific features of networks, are often used to represent and analyze network data as well as their mathematical descriptions. Chief among them, the configuration model constrains random networks by their degree distribution and is foundational to many areas of network science. However, these representations are often selected based on intuition or mathematical and computational simplicity rather than on statistical evidence. To evaluate the quality of a network representation we need to consider both the amount of information required by a random network model as well as the probability of recovering the original data when using the model as a generative process. To this end, we calculate the approximate size of network ensembles generated by the popular configuration model and its generalizations that include degree-correlations and centrality layers based on the onion decomposition. We then apply minimum description length as a model selection criterion and also introduce the Network Onion Divergence: model selection and network comparison over a nested family of configuration models with differing level of structural details. Using over 100 empirical sets of network data, we find that a simple Layered Configuration Model offers the most compact representation of the majority of real networks. We hope that our results will continue to motivate the development of intricate random network models that help capture network structure beyond the simple degree distribution.