Changing the ranking in eigenvector centrality of a weighted graph by small perturbations (Nicola Guglielmi, GSSI, L'Aquilla)

09.12.2025 14:00

We consider the problem of ranking nodes in a weighted graph based on eigenvector centrality. This measure assigns importance to each node according to the entries of the Perron eigenvector of the adjacency matrix. Our goal is to investigate how small perturbations of the edge weights affect this ranking, thereby revealing the robustness and sensitivity of the centrality measure. We formulate this as a matrix nearness problem, which is solved through an iterative algorithm. The approach provides quantitative insight into how fragile or stable a network’s hierarchy is under small structural changes.  
 This is based on joint projects with Michele Benzi (SNS, Pisa) and Christian Lubich (University of Tübingen). 

Lieu

Conseil Général 7-9, Room 1-05, Séminaire d'analyse numérique

entrée libre