内部演化网络分析

Analysis of inner evolving networks

分析了Barabasi-Albert(BA)无标度网络内部演化加边对网络结构的影响,考虑了线性和非线性择优连接.基于扩展的率方程方法,考虑引入新节点和内部加边引起的网络中已有节点的度的变化率,得到了度分布的精确表达式.当择优连接为线性时,度分布服从幂律;对于亚线性择优连接,度分布呈拉伸的指数分布形式.对于超线性择优连接,边的两端都择优连接会出现几乎与网络中其他所有节点都相连的"凝胶"节点.

The effects of inner edge addition on the structure of the Barabasi-Albert （BA）scale-free network are analyzed, with the linear and non-linear preferential attachment. Based on the extended rate equation approach, considering the changing rates of the existing nodes＇ degrees caused by the addition of new nodes and edges, the exact expressions for the degree distributions are obtained. When the preferential attachment is linear, the degree distributions follow the power-law form. For the sub-linear preferential attachment, the degree distributions follow the form of stretched exponential; for the suplinear preferential attachment, the double-end-point preferential attachment can lead to an extremely low number of ＂gel＂ nodes connecting to nearly every other node in the network. The results obtained provide references for further researches on other properties of inner evolving networks.