Inspired by real world phenomena, in this paper, the authors present a power law evolutional network model with degree exponent β < 2. Combinatorial probabilistic method is applied to the theoretical analysis of the presented model. In the proposed model, each time stamp the number of links among a newly added node and old ones follows Poisson distribution with parameter λ and selection probability p. The authors derive exact analytical relationship between the exponent of the power law β, the parameters λ and p. Simulation result is consistent with the exponent β analytical solution. Both theoretical analysis and simulation results show that the presented network evolution model has two obvious real world social network characteristics, degree exponent β < 2 and bending phenomena.

中文翻译：

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度指数<2的无标度社会网络演化模型研究

受现实世界现象的启发，作者提出了幂指数为β <2的幂律进化网络模型。将组合概率方法应用于该模型的理论分析。在提出的模型中，每个时间戳记新添加的节点和旧节点之间的链接数遵循具有参数λ和选择概率p的泊松分布。作者推导了幂律β的指数，参数λ和p之间的精确解析关系。仿真结果与指数β一致分析解决方案。理论分析和仿真结果均表明，本文提出的网络演化模型具有两个明显的现实世界社会网络特征：度指数β <2和弯曲现象。