非均齐超网络中标度律的涌现—–富者愈富导致幂律分布吗?

Emergence of scaling in non-uniform hypernetworks—–does “the rich get richer” lead to a power-law distribution?

建立非线性择优连接非均齐超网络演化模型,研究非均齐超网络演化机制和拓扑性质.使用Poisson过程理论和连续化方法对模型进行分析,给出超网络超度的特征方程.利用超度特征方程不仅证明网络稳态平均超度分布存在,而且获得超度分布的解析表达式.分析表明这个网络具有"富者愈富"现象.仿真实验和理论分析相符合.随着网络规模的增大,这个动态演化的非均齐超网络的超度分布表现出拉直指数分布的特征,而不一定是幂律分布.结果表明"富者愈富"不一定导致幂律分布.

In this paper, we propose a non-uniform hypernetwork moclel Wltll a nomu^e~r pivLv^c~l^l,~, ,~ , the evolving mechanism and topological properties of the hypernetwork. We analyze the model by using a Poisson process theory and a continuous technique, and give a characteristic equation of hyperdegrees, We obtain the stationary average hyperdegree distribution of the hypernetwork by the characteristic equation. The analytical result shows that the hypernetwork has a phenomenon of ＂the rich get richer＂, and it accords well with the simulation. It is shown in this paper that the hyperdegree distribution of the dynamic model exhibits a stretched exponential distribution with the increase of the hypernetwork size. It proves that ＂the rich get richer＂ does not necessarily induce a power-law distribution.