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.

翻译：中心性度量在网络分析中扮演着关键角色，而具体度量指标的选择会显著影响结论的准确性，因为每种度量都代表了节点重要性的独特概念。在已提出的400多种指标中，为特定应用选择最合适的度量仍然是一个挑战。现有方法——包括基于模型、数据驱动和公理化方法——存在局限性，需要针对每项具体应用关联模型、训练数据集或限制性公理。为解决这一问题，我们引入了剔除法，该方法依赖于专家对简单图中中心性行为的概念。剔除法包括：构建候选度量集合、生成尽可能小的图列表以区分不同度量、构建决策树调查问卷，并识别与专家概念一致的度量。我们将该方法应用于包含40种中心性的多样化集合（包括基于核的新指标），并与公理化方法相结合。值得注意的是，仅需13个小型1-树即可区分全部40种度量，即使是高度相似的成对度量也不例外。通过采用自洽性或桥梁公理等简单的序数公理，度量集合可大幅缩减，从而使剔除调查过程更加简短。应用剔除法为部分中心性指标（如PageRank、桥接中心性以及基于相异性的特征向量中心性等）提供了富有洞察力的发现。该方法在劳动力和时间成本方面具有经济性，可补充现有度量选择方法，并更深入地揭示中心性度量背后的内在机制。