Mixing patterns in networks

分类 混合模式 混合(物理) 顶点(图论) 统计物理学 计算机科学 标量(数学) 数学 复杂网络 物理 图形 组合数学 理论计算机科学 量子力学 几何学
作者
M. E. J. Newman
出处
期刊:Physical review 卷期号:67 (2) 被引量:2514
标识
DOI:10.1103/physreve.67.026126
摘要

We study assortative mixing in networks, the tendency for vertices in networks to be connected to other vertices that are like (or unlike) them in some way. We consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age. As a special example of the latter we consider mixing according to vertex degree, i.e., according to the number of connections vertices have to other vertices: do gregarious people tend to associate with other gregarious people? We propose a number of measures of assortative mixing appropriate to the various mixing types, and apply them to a variety of real-world networks, showing that assortative mixing is a pervasive phenomenon found in many networks. We also propose several models of assortatively mixed networks, both analytic ones based on generating function methods, and numerical ones based on Monte Carlo graph generation techniques. We use these models to probe the properties of networks as their level of assortativity is varied. In the particular case of mixing by degree, we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices.
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