Dynamical complexity as a proxy for the network degree distribution

TL;DR

This paper demonstrates that the dynamical complexity of nodes in a weakly coupled network correlates with their topological degree, enabling inference of the network's degree distribution from individual node dynamics.

Contribution

It introduces a method to infer network degree distribution solely from local dynamical measurements, linking topology and dynamics in complex systems.

Findings

Higher degree nodes exhibit lower dynamical complexity.

The relationship holds across different models and experimental setups.

Network degree distribution can be inferred from node dynamics.

Abstract

We explore the relation between the topological relevance of a node in a complex network and the individual dynamics it exhibits. When the system is weakly coupled, the effect of the coupling strength against the dynamical complexity of the nodes is found to be a function of their topological role, with nodes of higher degree displaying lower levels of complexity. We provide several examples of theoretical models of chaotic oscillators, pulse-coupled neurons and experimental networks of nonlinear electronic circuits evidencing such a hierarchical behavior. Importantly, our results imply that it is possible to infer the degree distribution of a network only from individual dynamical measurements.