Reconstruction of Directed Networks from Consensus Dynamics

TL;DR

This paper presents a novel method for reconstructing the topology of unknown directed networks from consensus dynamics by using a node-grounding approach and spectral density measurements, capable of identifying edges and directions.

Contribution

The paper introduces a new spectral-based reconstruction method that works with unknown spectral density and extends to directed networks, including undirected and unidirectional cases.

Findings

Reconstruction is possible using spectral densities from grounded and ungrounded systems.

Method can detect edge directions in directed networks.

Reconstruction simplifies for undirected or unidirectional networks without grounding.

Abstract

This paper addresses the problem of identifying the topology of an unknown, weighted, directed network running a consensus dynamics. We propose a methodology to reconstruct the network topology from the dynamic response when the system is stimulated by a wide-sense stationary noise of unknown power spectral density. The method is based on a node-knockout, or grounding, procedure wherein the grounded node broadcasts zero without being eliminated from the network. In this direction, we measure the empirical cross-power spectral densities of the outputs between every pair of nodes for both grounded and ungrounded consensus to reconstruct the unknown topology of the network. We also establish that in the special cases of undirected or purely unidirectional networks, the reconstruction does not need grounding. Finally, we extend our results to the case of a directed network assuming a general dynamics, and prove that the developed method can detect edges and their direction.