具有Hub聚集特性的分形网络优化模型分析

Optimization Model Analysis on Fractal Network with Hub Aggregation Property

针对一种双目标优化网络模型具有Hub节点聚集行为的现象,提出分形的涌现与Hub节点的聚集行为有关的结论。采用盒子覆盖法对该模型的3种优化网络进行重整化,验证该模型存在分形性和尺度不变性。进一步比较一些真实网络和优化网络的平均最短路径,分析骨架结构的分形临界条件。实验结果表明,分形网络只要满足结构平衡,就具有确定比例的Hub节点聚集和Hub节点排斥行为。

Aiming at the bi-objective optimization network model, which has the Hub node aggregation behaviors,the conclusion that the origin of the fractality is associated with the aggregation behaviors of Hub node is presented. The boxcovering method is used to regularize the three optimization networks of the model, verify fractal properties and scaleinvariance. The average shortest path of some real networks and optimized networks is further compared. The critical condition of the skeleton structure is analyses. Experimental result shows that as long as the structural equilibrium of the fractal network is satisfied, certain proportion of Hub node aggregation and Hub node exclusion behaviors is available.