  Centrality metrics play a crucial role in network analysis, while the choice
of specific measures significantly influences the accuracy of conclusions as
each measure represents a unique concept of node importance. Among over 400
proposed indices, selecting the most suitable ones for specific applications
remains a challenge. Existing approaches -- model-based, data-driven, and
axiomatic -- have limitations, requiring association with models, training
datasets, or restrictive axioms for each specific application. To address this,
we introduce the culling method, which relies on the expert concept of
centrality behavior on simple graphs. The culling method involves forming a set
of candidate measures, generating a list of as small graphs as possible needed
to distinguish the measures from each other, constructing a decision-tree
survey, and identifying the measure consistent with the expert's concept. We
apply this approach to a diverse set of 40 centralities, including novel
kernel-based indices, and combine it with the axiomatic approach. Remarkably,
only 13 small 1-trees are sufficient to separate all 40 measures, even for
pairs of closely related ones. By adopting simple ordinal axioms like
Self-consistency or Bridge axiom, the set of measures can be drastically
reduced making the culling survey short. Applying the culling method provides
insightful findings on some centrality indices, such as PageRank, Bridging, and
dissimilarity-based Eigencentrality measures, among others. The proposed
approach offers a cost-effective solution in terms of labor and time,
complementing existing methods for measure selection, and providing deeper
insights into the underlying mechanisms of centrality measures.
