How to choose the most appropriate centrality measure?
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We propose a new method to select the most appropriate network centrality measure based on the user's opinion on how such a measure should work on a set of simple graphs. The method consists in: (1) forming a set F of candidate measures; (2) generating a sequence of sufficiently simple graphs that distinguish all measures in F on some pairs of nodes; (3) compiling a survey with questions on comparing the centrality of test nodes; (4) completing this survey, which provides a centrality measure consistent with all user responses. The developed algorithms make it possible to implement this approach for any finite set F of measures. This paper presents its realization for a set of 40 centrality measures. The proposed method, called culling, can be used for rapid analysis or combined with a normative approach by compiling a survey on the subset of measures that satisfy certain normative conditions (axioms). In the present study, the latter was done for the subsets determined by the Self-consistency or Bridge axioms.
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