一种无标度超网络动态模型的建立与分析

Establishment and Analysis on a Class of Scale-free Hypernetworks Dynamic Model

基于超网络理论,构造了一个新的演化超网络,该网络包含新节点和新超边的增长、旧节点和旧超边的消失,亦包括超边的重连。在该超网络演化过程中,除了通过增加新节点来增长超边之外,还可以在旧节点之间构建新的超边。这种同时有增有减的进化超网络模型比只有增加的演化超网络模型更具有现实意义。利用泊松过程理论和连续化方法,得到了超网络的稳态平均超度分布和度分布。数值模拟的结果表明,演化超网络服从广义幂律分布,具有“倾向性地依附”的现象。对稳态平均超度分布的理论预测与数值模拟结果吻合较好。

Based on hypernetwork theory,we construct a new evolving hypernetwork,which incorporating new nodes and new hyperedges growing,old nodes and old hyperedges disappearing,or rewiring of hyperedges from some nodes to anothers.Besides the growth of hyperedges by adding new nodes,it is also possible that a new hyperedge can be constructed between old nodes in hypernetworks.This evolving hypernetwork model with both increasing and decreasing is more realistic than the evolving model only with increasing.By employing Poisson process theory and continuous method,we obtain stationary average hyperdegree distribution and degree distribution of the hypernetwork.Analytical result shows that the evolving hypernetwork following a generalized power-law distribution,has a phenomenon of“tendentiously attached”.The theoretical prediction of the stationary average hyperdegree distribution and degree distribution are in good agreement with the real numerical simulation results.