How to choose the most appropriate centrality measure?

We propose a new method for selecting the most appropriate network centrality measure based on the user's opinion on how such a measure should work on simple graphs. The method consists in: (1) forming a set $\cal F$ of candidate measures; (2) generating a list $\cal G$ of fairly simple graphs such that for every pair of measures in $\cal F$, the centrality rankings they define differ on some graph $G\in{\cal G}$; (3) compiling a survey that consists of questions on comparing the centrality of test nodes in some graphs $G\in{\cal G}$; (4) completing this survey, which yields a centrality measure consistent with all user responses. We develop algorithms that implement the proposed method, called culling, for an arbitrary finite set $\cal F$ that does not contain order-equivalent measures. The culling method can be used either for rapid analysis or in combination with a normative approach by compiling a survey on the subset of measures that satisfy chosen axioms. As an example, this method is applied to a set of forty diverse centrality measures. Abbreviated surveys are constructed on the subsets of measures that satisfy the Self-consistency or Bridge axioms.