Abstract
This paper studies the extent to which centrality measures share a common structure. In contrast with prior work, I take an ordinal approach, defining centrality measures as preorders that satisfy an axiom called recursive monotonicity. From this axiom, I derive two fundamental measures, strong and weak centrality, and I relate these to the equilibria of network games. Any equilibrium in a game of strategic complements implicitly orders the players by their actions. Strong centrality captures comparisons shared across all equilibria in all such games. Weak centrality captures comparisons shared across minimal and maximal equilibria in all such games.
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