精确计算派系网络的Mandelbrot系数  

Accurate Calculation of the Mandelbrot Coefficient to the Cliques Networks

作　　者：王旭文[1] 任学藻[1] 贺树[1] 廖旭[1] 

机构地区：[1]西南科技大学理学院,四川绵阳621010

出　　处：《复杂系统与复杂性科学》2012年第3期90-94,共5页Complex Systems and Complexity Science

摘　　要：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。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 net- works, 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＋coom） ^-y , where Mandelbrot pa- rameter is cq-1/2. By numerical simulation, we have found that both the parameter of Mandel- brot law and power-law exponent fit well with theoretical values.

关 键 词：m-派系 Mandelbrot分布律 Mandelbrot系数 

分 类 号：N93[自然科学总论] N94