Ordinal Centrality

Abstract

Centrality measures play a key role in network analysis. This paper studies the extent to which these measures share a common structure. In contrast with prior work, I take an ordinal approach, considering preorders on the vertex set of a graph that satisfy an intuitive axiom called recursive monotonicity. From this axiom, I derive two fundamental measures, strong centrality and weak centrality, and I relate these measures to the equilibria of network games. Any equilibrium in a network game of strategic complements induces an order on the players based on who takes higher actions. I show that strong centrality exactly captures the comparisons that are shared across all equilibria in all such games. I show that weak centrality captures those comparisons that are shared across the minimal and maximal equilibria in all such games.

Keywords: Centrality, networks, ordinal

JEL Classification: D85