Modeling critical connectivity constraints in random and empirical networks

TL;DR

This paper introduces a simple modeling approach that incorporates critical connectivity constraints into random network models, improving their ability to analyze network robustness and structure before damage occurs.

Contribution

It proposes a novel conceptual framework distinguishing critical and subcritical connections, capturing network structure with only one or two equations, enhancing existing models.

Findings

Single-equation approximation for sparse networks

Better modeling of network robustness before damage

Potential applications in infrastructure network analysis

Abstract

Random networks are a powerful tool in the analytical modeling of complex networks as they allow us to write approximate mathematical models for diverse properties and behaviors of networks. One notable shortcoming of these models is that they are often used to study processes in terms of how they affect the giant connected component of the network, yet they fail to properly account for that component. As an example, this approach is often used to answer questions such as how robust is the network to random damage but fails to capture the structure of the network before any inflicted damage. Here, we introduce a simple conceptual step to account for such connectivity constraints in existing models. We distinguish network neighbors into two types of connections that can lead or not to a component of interest, which we call critical and subcritical degrees. In doing so, we capture important structural features of the network in a system of only one or two equations. In particular cases where the component of interest is surprising under classic random network models, such as sparse connected networks, a single equation can approximate state-of-the art models like message passing which require a number of equations linear in system size. We discuss potential applications of this simple framework for the study of infrastructure networks where connectivity constraints are critical to the function of the system.