Inferring Network Topology from Complex Dynamics

TL;DR

This paper introduces a universal, noise-robust analytical method for inferring the topology of complex networks from a single, long dynamical observation without external intervention, applicable to diverse dynamical behaviors.

Contribution

The authors develop a direct, analytical approach to reconstruct network structure and parameters from observed trajectories, applicable to arbitrary dynamical systems with known functional forms.

Findings

Effective reconstruction of network topology from complex dynamics.

Method works with noisy data and various dynamical regimes.

Simultaneous inference of network structure and system parameters.

Abstract

Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation of one collective dynamical trajectory. The general theoretical framework is applicable to arbitrary network dynamical systems described by ordinary differential equations. No interference (external driving) is required and the type of dynamics is not restricted in any way. In particular, the observed dynamics may be arbitrarily complex; stationary, invariant or transient; synchronous or asynchronous and chaotic or periodic. Presupposing a knowledge of the functional form of the dynamical units and of the coupling functions between them, we present an analytical solution to the inverse problem of finding the network topology. Robust reconstruction is achieved in any sufficiently long generic observation of the system. We extend our method to simultaneously reconstruct both the entire network topology and all parameters appearing linear in the system's equations of motion. Reconstruction of network topology and system parameters is viable even in the presence of substantial external noise.