Ben Gurion University of the Negev, Be'er-Sheva, Israel.
Bar-Ilan University, Ramat Gan, Israel.
PLoS One. 2018 Oct 24;13(10):e0205820. doi: 10.1371/journal.pone.0205820. eCollection 2018.
A common two-tier structure for social networks is based on partitioning society into two parts, referred to as the elite and the periphery, where the "elite" is the relatively small but well-connected and highly influential group of powerful individuals around which the society is centered, and the "periphery" consists of the rest of society. It is observed that the relative sizes of economic and social elites in various societies appear to be continually declining. One possible explanation is that this is a natural social phenomenon, resembling Price's "square root" law for the fraction of good scientists in the scientific community. We try to assess the validity of this explanation by studying the elite-periphery structure via introducing a novel axiom-based model for representing and measuring the influence between the elite and the periphery. The model is accompanied by a set of axioms that capture the elite's dominance, robustness and density, as well as a compactness property. Relying on the model and the accompanying axioms, we are able to draw a number of insightful conclusions about the elite-periphery structure. In particular, we show that in social networks that respect our axioms, the size of a compact elite is sublinear in the network size. This agrees with Price's principle but appears to contradict the common belief that the elite size tends to a linear fraction of society (recently claimed to be around 1%). We propose a natural method to create partitions with nice properties, based on the key observation that an elite-periphery partition is at what we call a 'balance point', where the elite and the periphery maintain a balance of powers. Our method is based on setting the elite to be the k most influential nodes in the network and suggest the balance point as a tool for choosing k and therefore the size of the elite. When using nodes degrees to order the nodes, the resulting k-rich club at the balance point is the elite of a partition we refer to as the balanced edge-based partition. We accompany these findings with an empirical study on 32 real-world social networks, which provides evidence that balanced edge-based partitions which satisfying our axioms commonly exist.
常见的社交网络双层结构基于将社会分为两部分，分别称为精英和外围，其中“精英”是一个相对较小但联系紧密、影响力很大的有权势的个人群体，社会以之为中心，而“外围”则由社会的其他部分组成。人们观察到，各种社会中经济和社会精英的相对规模似乎在持续下降。一种可能的解释是，这是一种自然的社会现象，类似于普赖斯（Price）关于科学界优秀科学家比例的“平方根”定律。我们通过引入一种新的基于公理的模型来评估这种解释的有效性，该模型用于表示和衡量精英与外围之间的影响。该模型还附有一组公理，这些公理捕捉了精英的主导地位、稳健性和密度，以及紧凑性。依靠该模型和伴随的公理，我们能够就精英-外围结构得出许多有见地的结论。特别是，我们表明，在尊重我们的公理的社交网络中，紧凑精英的规模是网络规模的次线性。这与普赖斯（Price）的原则一致，但似乎与精英规模趋于社会线性分数的普遍信念相矛盾（最近声称约为 1%）。我们提出了一种创建具有良好属性分区的自然方法，其基础是关键观察结果，即精英-外围分区处于我们所谓的“平衡点”，其中精英和外围保持权力平衡。我们的方法基于将精英定义为网络中最有影响力的 k 个节点，并建议平衡点作为选择 k 的工具，从而选择精英的规模。当使用节点度对节点进行排序时，平衡点处的结果 k-丰富俱乐部是我们称为平衡边基分区的分区的精英。我们将这些发现与对 32 个真实社交网络的实证研究相结合，该研究提供了证据，表明满足我们公理的平衡边基分区普遍存在。
