Source-linked AI summary
Predicting criticality and dynamic range in complex networks: effects of topology
Daniel B. Larremore, Woodrow L. Shew, Juan G. Restrepo
TL;DR
The paper asks how network topology affects dynamic range in excitable networks and develops a theoretical framework to analyze that relationship. Combining spectral analysis with numerical simulations, it finds that criticality and maximum dynamic range occur at largest eigenvalue λ = 1, while more homogeneous topologies provide higher dynamic range.
Problem
The paper addresses why the mean-degree criterion for criticality fails in heterogeneous networks and how topology determines dynamic range.
Method
The authors analyze the Kinouchi-Copelli model using spectral properties of the weighted adjacency matrix, nonlinear approximations, and numerical simulations across network topologies.
Results
Criticality and peak dynamic range occur at largest eigenvalue λ = 1 across diverse tested topologies, while homogeneous networks achieve higher dynamic range than heterogeneous networks.
Takeaways & Limitations
The largest adjacency-matrix eigenvalue provides a topology-general criterion for criticality and dynamic range, with network homogeneity favoring greater dynamic range.
Takeaways & Limitations
The analysis assumes statistical independence among neighboring-node excitation events and approximates products exponentially when each node has many incoming connections near criticality.
Abstract
from arXiv · showhide
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.