A Complete Characterization of the Inverse Eigenvector Centrality Problem for Undirected Graphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918474497916928 |
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| author | Passacantando, Mauro Raciti, Fabio |
| author_facet | Passacantando, Mauro Raciti, Fabio |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26796 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Complete Characterization of the Inverse Eigenvector Centrality Problem for Undirected Graphs Passacantando, Mauro Raciti, Fabio Combinatorics 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. |
| title | A Complete Characterization of the Inverse Eigenvector Centrality Problem for Undirected Graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.26796 |