Selection of Centrality Measures Using Self-Consistency and Bridge Axioms

We consider several families of network centrality measures induced by graph kernels, which include some well-known measures and many new ones. The Self-consistency and Bridge axioms, which appeared earlier in the literature, are closely related to certain kernels and one of the families. We obtain a necessary and sufficient condition for Self-consistency, a sufficient condition for the Bridge axiom, indicate specific measures that satisfy these axioms, and show that under some additional conditions they are incompatible. PageRank centrality applied to undirected networks violates most conditions under study and has a property that according to some authors is ``hard to imagine'' for a centrality measure. We explain this phenomenon. Adopting the Self-consistency or Bridge axiom leads to a drastic reduction in survey time in the culling method designed to select the most appropriate centrality measures.Comment: 23 pages, 5 figures. A reworked versio

Random-Walk Closeness Centrality Satisfies Boldi-Vigna Axioms

Abstract. Recently Boldi and Vigna proposed axioms that would characterize good notions of centrality. We study a random-walk version of closeness centrality and prove that is satisfies Boldi-Vigna axioms for non-directed graphs

Axiomization of the center function on trees.

We give a new, short proof that four certain axiomatic properties uniquely define the center of a tree.