潜在收益作为中心性衡量标准
Potential gain as a centrality measure
摘要：
可导航性是与人工或自然系统相关的图形的显著特征，其主要目标是信息或货物的运输。我们说，图$\mathcal{G}$是可导航的代理是能够有效地达到任何目标节点在$\mathcal{G}$通过本地路由决策。在社交网络中，可导航性意味着通过个人联系人联系到个人的能力。图的可导航性已经得到了很好的研究，但一个基本的问题仍然是开放的：为什么有些人比其他人更有可能通过短的，朋友的朋友，通信链到达？在这篇文章中，我们回答了上述问题，提出了一个新的中心性度量称为潜在的增益，在非正式的意义上，量化了目标节点可以达到的容易程度。我们定义了两个变量的潜在增益，称为几何和指数的潜在增益，并提出快速算法来计算它们。几何增益和潜在增益是一类新的复合中心性度量的第一个实例，即，中心性度量，其将$\mathcal{G}$中的节点的流行度与其与所有其他节点的相似性相结合。正如以前的研究所示，流行度和相似性是调节人类在维基百科等大型网络中寻找信息的方式的两个主要标准。我们给出了一个正式的证明，一个节点的潜在收益总是相当于其度中心性（捕获流行）和卡茨中心性（捕获相似性）的产品。
英文摘要：
Navigability is a distinctive features of graphs associated with artificial or natural systems whose primary goal is the transportation of information or goods. We say that a graph $\mathcal{G}$ is navigable when an agent is able to efficiently reach any target node in $\mathcal{G}$ by means of local routing decisions. In a social network navigability translates to the ability of reaching an individual through personal contacts. Graph navigability is well-studied, but a fundamental question is still open: why are some individuals more likely than others to be reached via short, friend-of-a-friend, communication chains? In this article we answer the question above by proposing a novel centrality metric called the potential gain, which, in an informal sense, quantifies the easiness at which a target node can be reached. We define two variants of the potential gain, called the geometric and the exponential potential gain, and present fast algorithms to compute them. The geometric and the potential gain are the first instances of a novel class of composite centrality metrics, i.e., centrality metrics which combine the popularity of a node in $\mathcal{G}$ with its similarity to all other nodes. As shown in previous studies, popularity and similarity are two main criteria which regulate the way humans seek for information in large networks such as Wikipedia. We give a formal proof that the potential gain of a node is always equivalent to the product of its degree centrality (which captures popularity) and its Katz centrality (which captures similarity).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
