网络分析中的广义Erdos数
Generalized Erdos Numbers for network analysis
摘要：
在本文中，我们考虑的概念，在一个加权的网络，可以定义的拓扑结构，即使在没有一个度量节点之间的“接近度”。广义埃尔德斯数（GENs）满足许多期望的性质，作为当节点之间共享有限资源时的拓扑接近性的度量，因为它们是实值的和非局部的，并且可以用于创建非对称的连通矩阵。我们表明，它们可以用来定义一个个性化的衡量网络中节点的重要性与自然的解释，导致一个新的全球衡量中心性，是高度相关的页面排名。GEN的相对不对称性（由于其非度量定义）也与随机游走中节点之间的平均首次通过时间的不对称性有关，我们使用GEN的线性化形式来开发空间网络中“接近”的连续模型。作为其实用性的一个例子，我们部署它们来描述静态网络的结构，并显示它如何与网络上的动态在这种情况下，如流行病的传播。
英文摘要：
In this paper we consider the concept of `closeness' between nodes in a weighted network that can be defined topologically even in the absence of a metric. The Generalized Erdős Numbers (GENs) satisfy a number of desirable properties as a measure of topological closeness when nodes share a finite resource between nodes as they are real-valued and non-local, and can be used to create an asymmetric matrix of connectivities. We show that they can be used to define a personalized measure of the importance of nodes in a network with a natural interpretation that leads to a new global measure of centrality and is highly correlated with Page Rank. The relative asymmetry of the GENs (due to their non-metric definition) is linked also to the asymmetry in the mean first passage time between nodes in a random walk, and we use a linearized form of the GENs to develop a continuum model for `closeness' in spatial networks. As an example of their practicality, we deploy them to characterize the structure of static networks and show how it relates to dynamics on networks in such situations as the spread of an epidemic.
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