如何选择最合适的中心性度量？一种决策树方法
How to choose the most appropriate centrality measure? A decision tree approach
AI总结：
本文提出culling方法，通过决策树调查问卷和简单图区分40种中心性度量，仅需13个1-树即可完成区分，为选择最合适的中心性度量提供了低成本且高效的解决方案。
摘要：
中心性度量在网络分析中起着至关重要的作用，而具体度量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一种独特概念。在已提出的400多种指标中，为特定应用选择最合适的指标仍然是一个挑战。现有方法——基于模型的、数据驱动的和公理化的——都存在局限性，需要与模型关联、训练数据集或针对每个特定应用的限制性公理。为了解决这个问题，我们引入了culling方法，该方法依赖于专家关于简单图上中心性行为的概念。culling方法包括：形成一组候选度量，生成尽可能小的图列表以区分这些度量，构建决策树调查问卷，并识别与专家概念一致的度量。我们将这种方法应用于包含40种中心性的多样化集合，其中包括新颖的基于核的指标，并将其与公理化方法相结合。值得注意的是，仅需13个小的1-树就足以区分所有40种度量，即使是紧密相关的度量对也是如此。通过采用简单的序数公理，如Self-consistency或Bridge axiom，可以大幅缩减度量集合，使culling调查问卷变得简短。应用culling方法为一些中心性指标提供了有见地的发现，例如PageRank、Bridging和基于不相似性的Eigencentrality度量等。所提出的方法在劳动力和时间方面提供了一种成本效益高的解决方案，补充了现有的度量选择方法，并为理解中心性度量的底层机制提供了更深入的见解。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
