Predicting criticality and dynamic range in complex networks: effects of topology

TL;DR

This paper develops a theoretical framework linking network topology, specifically the largest eigenvalue of the adjacency matrix, to the dynamic range of excitable networks, revealing that homogeneous networks can achieve higher dynamic ranges.

Contribution

The study introduces a spectral approach to analyze how network topology influences dynamic range, highlighting the role of the largest eigenvalue and providing a generalization of previous models.

Findings

Largest eigenvalue of adjacency matrix governs dynamic range.

Critical regime with maximum dynamic range occurs at eigenvalue equal to one.

Homogeneous networks can attain higher dynamic range than heterogeneous ones.

Abstract

The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenvalue of the weighted network adjacency matrix governs the network dynamic range. Specifically, a largest eigenvalue equal to one corresponds to a critical regime with maximum dynamic range. We gain deeper insight on the effects of network topology using a nonlinear analysis in terms of additional spectral properties of the adjacency matrix. We find that homogeneous networks can reach a higher dynamic range than those with heterogeneous topology. Our analysis, confirmed by numerical simulations, generalizes previous studies in terms of the largest eigenvalue of the adjacency matrix.