Xu Xiao-Ke, Zhang Jie, Small Michael
School of Communication and Electronic Engineering, Qingdao Technological University, Qingdao 266520, People's Republic of China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Oct;82(4 Pt 2):046117. doi: 10.1103/PhysRevE.82.046117. Epub 2010 Oct 25.
Rich-club, assortativity and clustering coefficients are frequently used measures to estimate topological properties of complex networks. Here we find that the connectivity among a very small portion of the richest nodes can dominate the assortativity and clustering coefficients of a large network, which reveals that the rich-club connectivity is leveraged throughout the network. Our study suggests that more attention should be paid to the organization pattern of rich nodes, for the structure of a complex system as a whole is determined by the associations between the most influential individuals. Moreover, by manipulating the connectivity pattern in a very small rich-club, it is sufficient to produce a network with desired assortativity or transitivity. Conversely, our findings offer a simple explanation for the observed assortativity and transitivity in many real world networks--such biases can be explained by the connectivities among the richest nodes.
富俱乐部系数、关联性和聚类系数是常用于估计复杂网络拓扑特性的指标。在此我们发现，一小部分最富有的节点之间的连通性能够主导大型网络的关联性和聚类系数，这表明富俱乐部连通性在整个网络中发挥着作用。我们的研究表明，应更多关注富节点的组织模式，因为复杂系统的整体结构由最具影响力的个体之间的关联所决定。此外，通过操纵一个非常小的富俱乐部中的连通性模式，就足以生成具有所需关联性或传递性的网络。相反，我们的研究结果为许多现实世界网络中观察到的关联性和传递性提供了一个简单的解释——这种偏差可以由最富有节点之间的连通性来解释。
