局域演化的加权网络模型

Weighted Scale-Free Network Model with Evolving Local-World

在BA模型的基础上研究了兼顾局域演化、增长，以及局域与局域外存在较弱连接等3方面因素的加权网络。在这个模型中，引入了参数a，P1，P2，P3，通过理论分析，导出了这个加权网络模型的节点的强度分布，发现它服从幂律指数为2～3的幂律分布。数值仿真验证了理论分析的正确性；并通过调节参数，分析了该模型的内在特征和结构。这个改进的模型具有更为广泛的实际背景。

Basing on the BA scale-free model, we propose and study a weighted and evolving network, including the concept of local-world, the microscopic event of adding edges, and the weak links between the local-worlds. We design four parameters a,p1 ,P2 ,P3 in the model. Using continuum theory and rate equation method, we got the analytical expression of power-law strength distribution with the exponent γ∈[2,3]. The analytical expression is in good agreement with the numerical calculations. We also regulate the values of the parameters in order to uncover the characters and structure of network growing. This improved model has more broad practical backgrounds.