A Sieve Method for Consensus-type Network Tomography

TL;DR

This paper introduces a sieve method leveraging spectrum analysis and degree-based reconstruction to identify and characterize the interaction structure of networks with consensus dynamics, using ports for stimulation and observation.

Contribution

It proposes a novel sieve approach combining spectral and degree-based methods for network topology identification in consensus-type systems.

Findings

Successfully identifies key network features using spectral data.

Demonstrates the method's effectiveness through an example.

Provides a new tool for network tomography in multi-agent systems.

Abstract

In this note, we examine the problem of identifying the interaction geometry among a known number of agents, adopting a consensus-type algorithm for their coordination. The proposed identification process is facilitated by introducing "ports" for stimulating a subset of network vertices via an appropriately defined interface and observing the network's response at another set of vertices. It is first noted that under the assumption of controllability and observability of corresponding steered-and-observed network, the proposed procedure identifies a number of important features of the network using the spectrum of the graph Laplacian. We then proceed to use degree-based graph reconstruction methods to propose a sieve method for further characterization of the underlying network. An example demonstrates the application of the proposed method.