一个描述合作网络顶点度分布的模型

讨论一类社会合作网络以及一些与其拓扑结构相似的技术网络的度分布.建议一个最简化模型，通过解析的方法说明这些网络演化的共同动力学机理，而且说明顶点的度分布和项目度分布之间具有密切的一致关系，而项目所含的顶点数分布对度分布的影响较小；对模型的更一般情况进行数值模拟，说明上述结论具有一定的普遍性.这个模型显示这类广义的合作网络一般具有处于幂函数和指数函数这两种极端情况之间的度分布.简要介绍对一些实际合作网络做统计研究的结果，说明本模型的合理性. 关键词： 合作网络 度分布 项目度分布 项目含顶点数

A model describing the degree distribution of collaboration networks

This paper discusses the degree distribution of a type of social networks and some technological networks with similar topological structures. Firstly, we propose a most simplified model and try to show analytically that the degree distribution and the act degree distribution are well consistent, but the distribution of the number of the nodes inside an act have much smaller influence on the degree distribution. Secondly, we perform numerical simulations in a more general situation of the model, so as to show that the above mentioned conclusion is rather universal. This model leads to a conclusion that these generalized collaboration networks usually have a degree distribution between the power law and the exponential function. In the last part of the article, we introduce very briefly the results of the empirical statistical investigation on some practical collaboration networks to show that the model is valid for generalized collaboration networks.