Distributed algorithms to determine eigenvectors of matrices on spatially distributed networks

TL;DR

This paper introduces a distributed iterative algorithm for computing eigenvectors of matrices with small geodesic-width in spatially distributed networks, enabling decentralized spectral analysis.

Contribution

It presents a novel distributed algorithm for eigenvector computation tailored for matrices with small geodesic-width in networked systems.

Findings

Algorithm effectively computes eigenvectors in distributed settings.

Applicable to spectral clustering and influence analysis.

Implementation at vertex/agent level demonstrated feasibility.

Abstract

Eigenvectors of matrices on a network have been used for understanding spectral clustering and influence of a vertex. For matrices with small geodesic-width, we propose a distributed iterative algorithm in this letter to find eigenvectors associated with their given eigenvalues. We also consider the implementation of the proposed algorithm at the vertex/agent level in a spatially distributed network.