Mitchell Centre Seminar Series Martin Everett (Manchester) Assessing eigenvector type centrality for disconnected graphs.
| Dates: | 4 February 2026 |
|---|
| Times: | 16:00 - 17:30 |
|---|
| What is it: | Seminar |
|---|
| Organiser: | School of Social Sciences |
|---|
| Speaker: | Martin Everett |
|---|
|
|
Eigenvector centrality (Bonacich 1972) is one of the most used centrality measures in social network analysis. When applied to disconnected graphs, it typically assigns non-zero values only to nodes in the component with the largest eigenvalue, with all other nodes receiving zero. The usual solution is to calculate the dominant eigenvector for each component separately, but this creates difficulties when comparing centrality scores across components. This paper provides a comprehensive analysis of approaches to this problem, categorizing them into three types: (1) eigenvector computation on perturbed matrices that force connectivity, including epsilon perturbation, supernode augmentation, and PageRank; (2) algebraic generalizations that include eigenvector as a limiting case, such as Katz and Hubbell centrality; and (3) component-wise computation with various scaling factors. We propose 7 criteria to evaluate the methods. These criteria are grounded in properties that eigenvector centrality exhibits on connected graphs. We then propose two main rescaling approaches -- degree matching and beta matching -- and show that a quadratic variant of beta matching is the only method satisfying all seven evaluation criteria that we propose.
Travel and Contact Information
Find event
G7
Humanities Bridgeford Street
Manchester
