Supernodes: a generalization of the rich-club

IF 2.2 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of complex networks Pub Date : 2022-01-01 DOI:10.1093/comnet/cnab052

Su Yuan Chan;Kerri Morgan;Nicholas Parsons;Julien Ugon;Jonathan Crofts

引用次数: 0

Abstract

In this article, we present two new concepts related to subgraph counting where the focus is not on the number of subgraphs that are isomorphic to some fixed graph $H$ , but on the frequency with which a vertex or an edge belongs to such subgraphs. In particular, we are interested in the case where $H$ is a complete graph. These new concepts are termed vertex participation and edge participation, respectively. We combine these concepts with that of the rich-club to identify what we call a Super rich-club and rich edge-club. We show that the concept of vertex participation is a generalization of the rich-club. We present experimental results on randomized Erdös–Rényi and Watts–Strogatz small-world networks. We further demonstrate both concepts on a complex brain network and compare our results to the rich-club of the brain.

查看原文本刊更多论文

超级节点:富人俱乐部的概括

在本文中，我们提出了两个与子图计数有关的新概念，其中重点不是同构于某个固定图$H$的子图的数量，而是顶点或边属于此类子图的频率。特别是，我们对$H$是一个完整图的情况感兴趣。这些新概念分别被称为顶点参与和边缘参与。我们将这些概念与富裕俱乐部的概念相结合，以确定我们所称的超级富裕俱乐部和富裕边缘俱乐部。我们证明了顶点参与的概念是富裕俱乐部的一个推广。我们介绍了随机Erdös–Rényi和Watts–Strogatz小世界网络的实验结果。我们在复杂的大脑网络上进一步展示了这两个概念，并将我们的结果与大脑的丰富俱乐部进行了比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of complex networks MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.20

自引率

9.50%

发文量

期刊介绍： Journal of Complex Networks publishes original articles and reviews with a significant contribution to the analysis and understanding of complex networks and its applications in diverse fields. Complex networks are loosely defined as networks with nontrivial topology and dynamics, which appear as the skeletons of complex systems in the real-world. The journal covers everything from the basic mathematical, physical and computational principles needed for studying complex networks to their applications leading to predictive models in molecular, biological, ecological, informational, engineering, social, technological and other systems. It includes, but is not limited to, the following topics: - Mathematical and numerical analysis of networks - Network theory and computer sciences - Structural analysis of networks - Dynamics on networks - Physical models on networks - Networks and epidemiology - Social, socio-economic and political networks - Ecological networks - Technological and infrastructural networks - Brain and tissue networks - Biological and molecular networks - Spatial networks - Techno-social networks i.e. online social networks, social networking sites, social media - Other applications of networks - Evolving networks - Multilayer networks - Game theory on networks - Biomedicine related networks - Animal social networks - Climate networks - Cognitive, language and informational network