单偏好随机网络演化模型

Single Preferential Attachment Evolving Model of Scale-Free Networks

为了进一步探求复杂网络的形成机制,文章提出了一种B A(Barabási-A lbert)模型的扩展模型,考虑网络节点增加的同时,网络内部演化对网络发展的影响.该模型不仅包含加点、加边两种外部演化;而且还包含重连和删边两种内部演化,在每个时间步的操作中,新引入结点的度、重连的边数都是随机的.针对单偏好依附网络模型,运用连续性理论及随机分析理论证明,如果适当选取模型参数,这种网络自演化为无标度网络.而且验证了分析的结果与计算机模拟具有很好的一致性.

An extended model of BA mode is introduced in this paper. The network is evolved not only by the addition of new nodes, the addition of new links, but also by the rewiring and deleting of links. At every time step, the degree of the new nodes and the number of the rewiring links are random variables. With continuum and random theory, it has been proved that this model can self-organize into scale-free networks if the parameters are properly chosen. Finally, it has been found that the analytical expression is in good agreement with the numerical simulation results.