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arXiv · 2604.26796

A Complete Characterization of the Inverse Eigenvector Centrality Problem for Undirected Graphs

Mauro Passacantando·Fabio Raciti
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Abstract

We study the inverse eigenvector centrality problem on connected undirected graphs, namely, whether a given positive vector can be realized by assigning suitable edge weights. We provide a complete characterization in terms of stable sets and their neighborhoods, showing that the undirected case requires nontrivial global constraints absent in the directed setting.

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Mauro Passacantando, Fabio Raciti. 2026-04-29. A Complete Characterization of the Inverse Eigenvector Centrality Problem for Undirected Graphs. https://arxiv.org/abs/2604.26796

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