A Complete Characterization of the Inverse Eigenvector Centrality Problem for Undirected Graphs
Combinatorics
2026-04-30 v1
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.
Cite
@article{arxiv.2604.26796,
title = {A Complete Characterization of the Inverse Eigenvector Centrality Problem for Undirected Graphs},
author = {Mauro Passacantando and Fabio Raciti},
journal= {arXiv preprint arXiv:2604.26796},
year = {2026}
}