Modeling And Analysis Of Scale-free Network Base On Community Structure And Hierarchical Structure

As complex networks are widely applied to areas like mathematics, physics, engineering and so on, research on the quantitive and qualitative features of complex networks has always been a focus. Building a good network model is of great importance to the further research on complex networks. This thesis mainly considers the modeling of scale-free complex networks. Based on the improvement on BA model's growth and preferential mechanism, this thesis builds CHEN model (Community-Structured and Hierarchical-Structured Evolving Model), and other two improved models based on CHEN model:HEN model (Honeypot Evolving Model) and PEN model (Poisson Evolving Model).In the modeling of CHEN model, this thesis improves the preferential connection mechanism of BA model using turntable technique and degree limitation, optimizes the research in scale-free networks by bringing in hierarchical structure, and solves the uncertainty problem of local-world by using the community structure. Theoretical analysis proves that the degree distribution of CHEN model obeys power-law distribution and its power-law index is adjustable. Simulation experiment shows that CHEN model has a smaller average path length and a larger clustering coefficient. CHEN model improved the defect of BA model that its power-law index is an invariable3and its clustering coefficient is too small.This thesis brought up with two improved models in the light of the two shortcomings of CHEN model which are the fragility under intentional attack and the arrival of nodes evenly over time. Applying Honeypot technique of network security to CHEN model, the first improved model is generated—HEN model, which enhances the robustness and improved the fragility of CHEN model. Applying the phenomenon that nodes arrive in a Poisson process in queuing to CHEN model, the second improved model is generated—PEN model. And the transient degree distribution and the stationary mean degree distribution are generated through strict theoretical reasoning, which proves that PEN model is also a scale-free model.