精确计算派系网络的Mandelbrot系数

研究了派系连接生成的复杂网络的拓扑性质。解析得到了m-派系网络的度分布和累积度分布函数,发现最小度的概率总是1/2。在度较大时,度分布的近似解析解服从Zipf-Mandelbrot分布律,度分布的幂律指数为(2m-1)/(m-1),Mandelbrot系数为m(5-2m)/(2m-2)。累积度分布为(k+ccum)-γ+1,Mandel-brot系数为c+1/2。数值模拟发现,所得Mandelbrot系数和幂律指数与理论值符合得很好。

Accurate Calculation of the Mandelbrot Coefficient to the Cliques Networks

We have studied the topological property of the complex networks based on cliques.We have got the degree distribution and cumulative degree distribution functions of m-cliques networks,and found that the probability for the minimum degree is always 1/2.For larger degree,the degree distribution from approximately analytical solution obeys Zipf-Mandelbrot law,where the power-law exponent of degree distribution is(2m-1)/(m-1),and Mandelbrot parameter is m(5-2m)/(2m-2).The cumulative degree distribution is(k+ccum)-γ+1,where Mandelbrot parameter is c+1/2.By numerical simulation,we have found that both the parameter of Mandelbrot law and power-law exponent fit well with theoretical values.