Reconstructing Network Structures from Partial Measurements

TL;DR

This paper introduces a method to infer the structure of a network of interacting agents using velocity signal correlations, especially when only a subset of agents is measurable, improving efficiency over traditional approaches.

Contribution

The study demonstrates that velocity signal correlators can reveal network structure and geodesic distances among measurable agents, even with partial data, and offers a more efficient inference method.

Findings

Velocity correlators encode network structure and distances.

Method works with partial measurements of agents.

More efficient than traditional matrix-inversion approaches.

Abstract

The dynamics of systems of interacting agents is determined by the structure of their coupling network. The knowledge of the latter is, therefore, highly desirable, for instance, to develop efficient control schemes, to accurately predict the dynamics, or to better understand inter-agent processes. In many important and interesting situations, the network structure is not known, however, and previous investigations have shown how it may be inferred from complete measurement time series on each and every agent. These methods implicitly presuppose that, even though the network is not known, all its nodes are. Here, we investigate the different problem of inferring network structures within the observed/measured agents. For symmetrically coupled dynamical systems close to a stable equilibrium, we establish analytically and illustrate numerically that velocity signal correlators encode not only direct couplings, but also geodesic distances in the coupling network within the subset of measurable agents. When dynamical data are accessible for all agents, our method is furthermore algorithmically more efficient than the traditional ones because it does not rely on matrix inversion.