Linking the network centrality measures closeness and degree
Linking the network centrality measures closeness and degree
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DOI：
10.1038/s42005-022-00949-5
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发表时间：
2022-07-02
影响因子：
5.5
通讯作者：
Chen, Bingsheng
中科院分区：
文献类型：
--
作者：
Evans, Tim S.;Chen, Bingsheng
用中心性度量来度量网络中节点的重要性是任何网络应用中的核心任务。有许多可用的措施，据推测，许多编码类似的信息。我们给出了一个明确的非线性关系的两个最流行的措施节点的中心性：度和接近度。基于最短路径树近似，我们给出了一个解析推导，表明接近度的倒数线性依赖于度的对数。我们表明，我们的假设适用于一系列随机网络模型和来自130个真实世界的数据集的网络。我们将我们的结果与其他网络距离尺度（如平均距离）的先前结果相关联。我们的研究结果意味着，测量亲密度是广泛冗余的，除非我们的关系是用来消除依赖程度的亲密度。我们的关系的成功表明，大多数网络可以近似为最短路径生成树，这些树在统计上都是相似的，距离它们的根节点有两步或更多步。大量数据的可用性使网络科学成为跨学科的工具。作者推导出一个数学近似，将图论中最常用的两个中心性度量（度和接近度）联系起来，发现接近度的倒数线性依赖于度的对数;这种关系也用真实的世界网络进行了测试，发现吻合良好。
Measuring the importance of nodes in a network with a centrality measure is an core task in any network application. There many measures available and it is speculated that many encode similar information. We give an explicit non-linear relationship between two of the most popular measures of node centrality: degree and closeness. Based on a shortest-path tree approximation, we give an analytic derivation that shows the inverse of closeness is linearly dependent on the logarithm of degree. We show that our hypothesis works well for a range of networks produced from stochastic network models and for networks derived from 130 real-world data sets. We connect our results with previous results for other network distance scales such as average distance. Our results imply that measuring closeness is broadly redundant unless our relationship is used to remove the dependence on degree from closeness. The success of our relationship suggests that most networks can be approximated by shortest-path spanning trees which are all statistically similar two or more steps away from their root nodes.The availability of large amount of data has made network science a tool to be used across many disciplines. The authors derive a mathematical approximation that link two of the most used centrality measures in graph theory, degree and closeness, finding that the inverse of closeness is linearly dependent on the logarithm of degree; this relationship is also tested with real world networks finding good agreement.