从Caesar到Twitter：社交网络精英的公理化研究
From Caesar to Twitter: An Axiomatic Approach to Elites of Social Networks
摘要：
在许多社会中，都有一个精英，一个相对较小的群体，由有权势的个人组成，他们关系密切，影响力很大。从古罗马凯撒大帝的元老院到最近Twitter上的名人，精英的规模是相互冲突的社会力量竞相增加或减少的结果。本文的主要贡献是回答了均衡时精英的规模有多大的问题。我们采取一个公理化的方法来解决这个问题：假设一个精英存在，它是有影响力的，稳定的，无论是最小的或密集的，我们证明了它的大小必须是$Θ(\sqrt{m})$（其中$m$是在网络中的边缘的数量）。作为一个近似的精英，我们提出了一个实证研究的九个大型现实世界中的网络的子图形成的最高程度的节点，也被称为丰富的俱乐部。我们的研究结果表明，精英属性，如不成比例的影响力，稳定性和密度的$Θ(\sqrt{m})$丰富的俱乐部是普遍的属性，并应加入一个越来越多的共同现象的列表所共有的社交网络和复杂的系统，如“小世界”，幂律度分布，高集群，等。
英文摘要：
In many societies there is an elite, a relatively small group of powerful individuals that is well-connected and highly influential. Since the ancient days of Julius Caesar's senate of Rome to the recent days of celebrities on Twitter, the size of the elite is a result of conflicting social forces competing to increase or decrease it. The main contribution of this paper is the answer to the question how large the elite is at equilibrium. We take an axiomatic approach to solve this: assuming that an elite exists and it is influential, stable and either minimal or dense, we prove that its size must be $Θ(\sqrt{m})$ (where $m$ is the number of edges in the network). As an approximation for the elite, we then present an empirical study on nine large real-world networks of the subgraph formed by the highest degree nodes, also known as the rich-club. Our findings indicate that elite properties such as disproportionate influence, stability and density of $Θ(\sqrt{m})$-rich-clubs are universal properties and should join a growing list of common phenomena shared by social networks and complex systems such as "small world," power law degree distributions, high clustering, etc.
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。
