一种基于超图复杂网络的新的演化模型

A New Evolving Model for Hypergraph-Structure-Based Complex Networks

在超图理论的基础上,构建了一种新的复杂网络动态演化模型:在演化过程中,不仅有新节点和新边增加,也有旧节点和旧边消失,而除了新节点的加入可生成新边,网络中的老节点之间也可产生新的连接。上述基于超图的有增有减的动态演化模型比单纯增长的演化模型更具现实性。使用连续化方法和平均场理论对模型进行了分析,给出超网络超度的特征方程。利用超度特征方程,得到超度分布的解析表达式。仿真结果和理论分析一致,表明随着网络规模的增大,这个动态演化模型的超度分布符合幂律形式,具有无标度特性。

Based on the hypergraph theory,we constructed a new evolving model for complex networks： there are not only the new nodes and new edges growing,but also the old nodes and old edges disappearing. Besides the hyperedge growth by adding the new nodes,it is also possible that a new link can be constructed between the old nodes in networks. This evolving model with both increasing and decreasing is more realistic than the model only with increasing. Using a continuous technique and the mean field theory,we analyzed this model and gave a characteristic equation of hyperdegrees. We obtained an analytical expression of hyperdegree distribution by the characteristic equation,and it accords well with the simulation. The result shows that with the increase of the hypernetwork size,the hyperdegree distribution of this evolving model follows apow-law and scale-free law.