设计无标度网络的一种新方法

Novel approach to design scale-free networks

提出了一种设计生成满足任意指定幂律要求的无标度网络的新方法.该方法利用了无标度网络的一个重要性质,即无标度网络的最终形成是受其度的几何均值控制的.为此提出了一个算法,该算法从一个合理的小世界网络开始,通过富者愈富的原则不断地对当前网络实施删边和加边操作,同时保证网络中的节点个数、网络中的总边数和网络的连通性不变,直到网络中节点度的几何均值达到了一个特定的值为止,生成一个预定的无标度网络.数据仿真验证了该方法总可以生成一个满足指定幂律要求的无标度网络.

A novel approach is proposed that leads to the design and evolution of a scale-free network that satisfies any given power-law distribution. The approach makes use of another important feature of the scale-free network： the final formation of a scale-free network is controlled by the geometric mean of its degrees. Therefore, an algorithm is provided： starting from a rational smalbworld net- work, continuously deleting or adding an edge from or to the network by the ＂rich get richer＂ principle, meanwhile keeping the total number of nodes, the total number of edges and the connectivity of the network unchanged, until the geometric mean of the degrees of the network reaches a certain value, a prerequisite scale-free network will be formed. Numerical simulations show that the above algorithm can always lead to the evolution of a scale-free network that satisfies any given power-law distribution.