Empirical Networks are Sparse: Enhancing Multi-Edge Models with Zero-Inflation

TL;DR

This paper demonstrates that real-world networks are inherently sparse with many disconnected pairs, and traditional models fail to capture this, but incorporating zero-inflation significantly improves their accuracy in representing empirical data.

Contribution

The paper introduces zero-inflation into classical multi-edge network models to better capture the sparsity observed in real-world networks.

Findings

Zero-inflated models better fit empirical network data.

Traditional models underestimate network sparsity.

Zero-inflation accounts for excess zeroes in data.

Abstract

Real-world networks are sparse. As we show in this article, even when a large number of interactions is observed, most node pairs remain disconnected. We demonstrate that classical multi-edge network models, such as the $G(N,p)$, configuration models, and stochastic block models, fail to accurately capture this phenomenon. To mitigate this issue, zero-inflation must be integrated into these traditional models. Through zero-inflation, we incorporate a mechanism that accounts for the excess number of zeroes (disconnected pairs) observed in empirical data. By performing an analysis on all the datasets from the Sociopatterns repository, we illustrate how zero-inflated models more accurately reflect the sparsity and heavy-tailed edge count distributions observed in empirical data. Our findings underscore that failing to account for these ubiquitous properties in real-world networks inadvertently leads to biased models that do not accurately represent complex systems and their dynamics.