演化网络模型中的巨分支相变

提出了一个演化无标度网络模型,研究了网络中出现巨连通分支的相变.在模型中每步加入一个新节点,其带的边数服从泊松分布,这些边按照择优连接机制与网络中的旧节点进行连接.通过求解网络中连通分支演化满足的率方程,得到了网络中出现巨分支的条件,给出了模型的完整相变图.相变点表达式说明择优连接机制有助于巨分支的产生.

Giant Component Phase Transition in an Evolving Network

An evolving scale-free network is presented and the emergence of the giant connected component in it is studied. At each step a new node is added with a random number of edges linking to existing nodes according to the preferential attachment rule. By solving the rate equation of connected components, the critical value of the phase transition and the phase diagram of the model are obtained. The critical value is reduced with increasing tendency for preferential attachment.