Newman M E J
Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, Michigan 48109, USA.
Phys Rev Lett. 2009 Jul 31;103(5):058701. doi: 10.1103/PhysRevLett.103.058701. Epub 2009 Jul 27.
We offer a solution to a long-standing problem in the theory of networks, the creation of a plausible, solvable model of a network that displays clustering or transitivity--the propensity for two neighbors of a network node also to be neighbors of one another. We show how standard random-graph models can be generalized to incorporate clustering and give exact solutions for various properties of the resulting networks, including sizes of network components, size of the giant component if there is one, position of the phase transition at which the giant component forms, and position of the phase transition for percolation on the network.
我们为网络理论中一个长期存在的问题提供了一个解决方案，即创建一个合理的、可求解的网络模型，该模型展示聚类或传递性——网络节点的两个邻居也倾向于成为彼此的邻居。我们展示了如何将标准随机图模型进行推广以纳入聚类，并给出了所得网络各种属性的精确解，包括网络组件的大小、如果存在巨型组件则其大小、巨型组件形成时相变的位置以及网络上渗流相变的位置。
