A Centrality Measure Using Magnitude Homology
This study addresses the problem of effectively measuring node centrality in graphs from geometric and topological perspectives. To this end, it introduces magnitude homology—a novel application in graph centrality analysis—and proposes a local centrality measure grounded in relative homology: the importance of a node is quantified by the change in magnitude homology resulting from its removal. The proposed measure satisfies several natural axioms, exhibits favorable theoretical properties, and demonstrates unique effectiveness in experiments, offering complementary insights to classical centrality metrics. This work thus provides a new topological lens for evaluating node importance in complex networks.