Selection of Centrality Measures Using Self-Consistency and Bridge Axioms

TL;DR

This paper analyzes various network centrality measures induced by graph kernels, exploring axioms like Self-consistency and Bridge, and their implications for measure selection and properties such as PageRank's behavior.

Contribution

It provides necessary and sufficient conditions for these axioms, identifies measures satisfying them, and demonstrates how axioms influence centrality measure selection.

Findings

PageRank violates most axioms studied

Axioms significantly reduce survey time for measure selection

Certain measures are incompatible under specific conditions

Abstract

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.