论文标题
Gromov中心地位：使用三角不平等的多尺度衡量网络中心性
Gromov Centrality: A Multi-Scale Measure of Network Centrality Using Triangle Inequality Excess
论文作者
论文摘要
中心度测量基于不同的几何或扩散属性，量化网络中节点的重要性，并专注于不同的尺度。在这里，我们采用几何观点来定义网络中的多尺度中心性。给定节点之间的度量距离，我们通过三角形不平等的概念过分的概念来测量一个节点的趋势接近其附近节点之间的大地测量的趋势。根据邻域的大小，由此产生的Gromov中心性定义了图表中不同尺度上节点的重要性，并作为众所周知的概念（例如聚类系数和紧密度中心性）恢复。我们认为，格罗莫夫的中心性受网络的几何和边界约束的影响，并说明了它如何帮助区分随机几何图和经验传输网络中不同类型的节点。
Centrality measures quantify the importance of a node in a network based on different geometric or diffusive properties, and focus on different scales. Here, we adopt a geometrical viewpoint to define a multi-scale centrality in networks. Given a metric distance between the nodes, we measure the centrality of a node by its tendency to be close to geodesics between nodes in its neighborhood, via the concept of triangle inequality excess. Depending on the size of the neighborhood, the resulting Gromov centrality defines the importance of a node at different scales in the graph, and recovers as limits well-known concept such as the clustering coefficient and closeness centrality. We argue that Gromov centrality is affected by the geometric and boundary constraints of the network, and illustrate how it can help distinguish different types of nodes in random geometric graphs and empirical transportation networks.
