We propose a new method for selecting the most appropriate network centrality measure based on the user's opinion on how such a measure should work on simple graphs. The method consists in: (1) forming a set $\cal F$ of candidate measures; (2) generating a list $\cal G$ of fairly simple graphs such that for every pair of measures in $\cal F$, the centrality rankings they define differ on some graph $G\in{\cal G}$; (3) compiling a survey that consists of questions on comparing the centrality of test nodes in some graphs $G\in{\cal G}$; (4) completing this survey, which yields a centrality measure consistent with all user responses. We develop algorithms that implement the proposed method, called culling, for an arbitrary finite set $\cal F$ that does not contain order-equivalent measures. The culling method can be used either for rapid analysis or in combination with a normative approach by compiling a survey on the subset of measures that satisfy chosen axioms. As an example, this method is applied to a set of forty diverse centrality measures. Abbreviated surveys are constructed on the subsets of measures that satisfy the Self-consistency or Bridge axioms.
翻译:我们提出了一种新方法,用于选择最合适的网络中心性度量,该方法基于用户对这类度量在简单图上的表现方式的看法。该方法包括:(1) 构建一个候选度量集合 $\cal F$;(2) 生成一个较为简单图的列表 $\cal G$,使得对于 $\cal F$ 中的每一对度量,它们所定义的中心性排名在某个图 $G\in{\cal G}$ 上存在差异;(3) 编制一份调查问卷,内容涉及比较某些图 $G\in{\cal G}$ 中测试节点的中心性;(4) 完成该调查问卷,从而得到与所有用户响应一致的度量。我们开发了实现所提方法(称为“筛选法”)的算法,适用于任意不含顺序等价度量的有限集合 $\cal F$。该筛选法既可单独用于快速分析,也可与规范性方法结合使用,即仅对满足特定公理条件的度量子集编制调查问卷。以一组四十种不同的中心性度量为例,我们针对满足自洽性公理或桥接公理的度量子集构建了简化版调查问卷。