The role of adjacency matrix degeneration in maximum entropy weighted network models

TL;DR

This paper investigates how the degeneration of adjacency matrices affects maximum entropy models of weighted networks, emphasizing the importance of accurate configuration counting for unbiased null models.

Contribution

It introduces a detailed analysis of adjacency matrix degeneration effects on entropy-based network models, highlighting the impact of different assumptions on network statistics.

Findings

Different assumptions lead to distinct network statistics.

Accurate configuration counting is crucial for unbiased models.

Differences are observable in real data applications.

Abstract

Complex network null models based on entropy maximization are becoming a powerful tool to characterize and analyze data from real systems. However, it is not easy to extract good and unbiased information from these models: A proper understanding of the nature of the underlying events represented in them is crucial. In this paper we emphasize this fact stressing how an accurate counting of configurations compatible with given constraints is fundamental to build good null models for the case of networks with integer valued adjacency matrices constructed from aggregation of one or multiple layers. We show how different assumptions about the elements from which the networks are built give rise to distinctively different statistics, even when considering the same observables to match those of real data. We illustrate our findings by applying the formalism to three datasets using an open-source software package accompanying the present work and demonstrate how such differences are clearly seen when measuring network observables.