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Centrality metrics play a crucial role in network analysis, while the choiceof specific measures significantly influences the accuracy of conclusions aseach measure represents a unique concept of node importance. Among over 400proposed indices, selecting the most suitable ones for specific applicationsremains a challenge. Existing approaches -- model-based, data-driven, andaxiomatic -- have limitations, requiring association with models, trainingdatasets, or restrictive axioms for each specific application. To address this,we introduce the culling method, which relies on the expert concept ofcentrality behavior on simple graphs. The culling method involves forming a setof candidate measures, generating a list of as small graphs as possible neededto distinguish the measures from each other, constructing a decision-treesurvey, and identifying the measure consistent with the expert's concept. Weapply this approach to a diverse set of 40 centralities, including novelkernel-based indices, and combine it with the axiomatic approach. Remarkably,only 13 small 1-trees are sufficient to separate all 40 measures, even forpairs of closely related ones. By adopting simple ordinal axioms likeSelf-consistency or Bridge axiom, the set of measures can be drasticallyreduced making the culling survey short. Applying the culling method providesinsightful findings on some centrality indices, such as PageRank, Bridging, anddissimilarity-based Eigencentrality measures, among others. The proposedapproach offers a cost-effective solution in terms of labor and time,complementing existing methods for measure selection, and providing deeperinsights into the underlying mechanisms of centrality measures.

How to choose the most appropriate centrality measure? A decision tree approach