A local eigenvector centrality

Abstract

Eigenvector centrality is an established measure of global connectivity, from which the importance and influence of nodes can be inferred. We introduce local eigenvector centrality (LEC), a scale-adaptive extension that integrates local and global connectivity into a single centrality measure. LEC identifies a topologically relevant mesoscopic scale for community-level centrality assessment, informed by prominent eigengaps, and combines information from the associated eigenvectors, via the Euclidean norm, to yield a centrality that reflects community-driven node influence. Networks with known community structures are employed to demonstrate that LEC closely reproduces eigenvector centrality for each community in isolation. Discrepancies between these measures are shown to be attributable to the global connectivity of affected nodes. LEC therefore provides a principled integration of community-level and global notions of node importance. Comparisons with PageRank and Katz centrality demonstrate that damping-based approaches do not recover community-scale centrality as effectively as LEC.

arXiv comment19 pages, 9 figures