Network Inference from Consensus Dynamics

TL;DR

This paper introduces a convex optimization approach leveraging spectral graph theory to accurately infer the structure of an unknown network from observed consensus dynamics across multiple topics, with proven consistency and demonstrated effectiveness.

Contribution

It presents a novel convex optimization framework that incorporates spectral properties to recover network topology from opinion data, addressing under-determinacy issues.

Findings

Method accurately recovers synthetic networks.

Method effectively infers real-world network structures.

Theoretical proof of consistency as the number of topics increases.

Abstract

We consider the problem of identifying the topology of a weighted, undirected network $\mathcal G$ from observing snapshots of multiple independent consensus dynamics. Specifically, we observe the opinion profiles of a group of agents for a set of $M$ independent topics and our goal is to recover the precise relationships between the agents, as specified by the unknown network $\mathcal G$. In order to overcome the under-determinacy of the problem at hand, we leverage concepts from spectral graph theory and convex optimization to unveil the underlying network structure. More precisely, we formulate the network inference problem as a convex optimization that seeks to endow the network with certain desired properties -- such as sparsity -- while being consistent with the spectral information extracted from the observed opinions. This is complemented with theoretical results proving consistency as the number $M$ of topics grows large. We further illustrate our method by numerical experiments, which showcase the effectiveness of the technique in recovering synthetic and real-world networks.