Network Topology Identification from Spectral Templates
Santiago Segarra, Antonio G. Marques, Gonzalo Mateos, and Alejandro, Ribeiro

TL;DR
This paper introduces a convex optimization approach to infer network topology from spectral templates, enabling efficient recovery of graph structures like adjacency matrices and Laplacians, with applications in brain network analysis.
Contribution
It proposes a novel method leveraging spectral templates for topology inference, including algorithms and conditions for identifying key graph shifts such as adjacency and Laplacian matrices.
Findings
Effective recovery of synthetic networks demonstrated.
Successful application to structural brain networks.
Algorithms show robustness and efficiency in various scenarios.
Abstract
Network topology inference is a cornerstone problem in statistical analyses of complex systems. In this context, the fresh look advocated here permeates benefits from convex optimization and graph signal processing, to identify the so-termed graph shift operator (encoding the network topology) given only the eigenvectors of the shift. These spectral templates can be obtained, for example, from principal component analysis of a set of graph signals defined on the particular network. The novel idea is to find a graph shift that while being consistent with the provided spectral information, it endows the network structure with certain desired properties such as sparsity. The focus is on developing efficient recovery algorithms along with identifiability conditions for two particular shifts, the adjacency matrix and the normalized graph Laplacian. Application domains include network…
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