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THE BOW-TIE CENTRALITY: A NOVEL MEASURE FOR DIRECTED AND WEIGHTED NETWORKS WITH AN INTRINSIC NODE PROPERTY
Advances in Complex Systems ( IF 0.4 ) Pub Date : 2019-12-27 , DOI: 10.1142/s0219525919500188
JAMES B. GLATTFELDER 1
Affiliation  

Today, there exist many centrality measures for assessing the importance of nodes in a network as a function of their position and the underlying topology. One class of such measures builds on eigenvector centrality, where the importance of a node is derived from the importance of its neighboring nodes. For directed and weighted complex networks, where the nodes can carry some intrinsic property value, there have been centrality measures proposed that are variants of eigenvector centrality. However, these expressions all suffer from shortcomings. Here, an extension of such centrality measures is presented that remedies all previously encountered issues. While similar improved centrality measures have been proposed as algorithmic recipes, the novel quantity that is presented here is a purely analytical expression, only utilizing the adjacency matrix and the vector of node values. The derivation of the new centrality measure is motivated in detail. Specifically, the centrality itself is ideal for the analysis of directed and weighted networks (with node properties) displaying a bow-tie topology. The novel bow-tie centrality is then computed for a unique and extensive real-world dataset, coming from economics. It is shown how the bow-tie centrality assesses the relevance of nodes similarly to other eigenvector centrality measures, while not being plagued by their drawbacks in the presence of cycles in the network.

中文翻译:

领结中心性:具有内在节点属性的定向和加权网络的新度量

今天,存在许多中心性度量来评估网络中节点的重要性,作为它们的位置和底层拓扑的函数。一类此类措施建立在特征向量中心性之上,其中节点的重要性源自其相邻节点的重要性。对于节点可以携带一些内在属性值的有向和加权复杂网络,已经提出了中心性度量,它们是特征向量中心性的变体。然而,这些表达方式都有缺点。在这里,提出了这种中心性措施的扩展,以解决所有以前遇到的问题。虽然已经提出了类似的改进中心性度量作为算法配方,但这里提出的新数量是纯粹的分析表达式,仅利用邻接矩阵和节点值向量。新的中心性度量的推导是详细的。具体来说,中心性本身非常适合分析显示蝴蝶结拓扑的有向和加权网络(具有节点属性)。然后为来自经济学的独特而广泛的真实世界数据集计算新颖的领结中心性。展示了蝴蝶结中心性如何与其他特征向量中心性度量类似地评估节点的相关性,同时在网络中存在循环时不受其缺点的困扰。然后为来自经济学的独特而广泛的真实世界数据集计算新颖的领结中心性。展示了蝴蝶结中心性如何与其他特征向量中心性度量类似地评估节点的相关性,同时在网络中存在循环时不受其缺点的困扰。然后为来自经济学的独特而广泛的真实世界数据集计算新颖的领结中心性。展示了蝴蝶结中心性如何与其他特征向量中心性度量类似地评估节点的相关性,同时在网络中存在循环时不受其缺点的困扰。
更新日期:2019-12-27
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