Research On Propagation And Improvement Of Null Model Algorithms In Complex Networks

The complex network null model abstracts the actual characteristics of some networks and and can be compared with the initial network.The problem of propagation in dynamics has always been a keystone in complex networks.It is of practical significance to use various methods to study complex network transmission.Firstly,this paper introduces the basic concepts,construction methods,related algorithms and applications of the null model.Then,according to the actual situation,the existing different order of null model algorithms are improved.Finally,the epidemic and rumor propagation in complex networks are studied with the generated null.The contributions of this paper are summarized as follows:1.Aiming at the problem that it is difficult to obtain a 2.5K null model network generated by the 2K null model generated by the existing 2K null model algorithm,a C-2KT algorithm(C represents clustering,2K represents second-order network,T represents triangle)is proposed.In the process of generating a new network from scratch,the C-2KT algorithm strategically regenerates the corresponding high-cluster 2K null model by considering the actual distribution of the node clustering spectrum.The experimental results verify that the C-2KT algorithm can generate a 2K null model with high clustering and closer to the original network clustering spectrum.When this 2K null model is used as the initial network,it is easier to reach the 2.5K null model.2.The recent 2.5K null model generation algorithm performs well for low-cluster networks,but for high-cluster networks,it often fails to achieve the desired goal.Then TS-MCMC algorithm is proposed(TS stands for taboo search and MCMC stands for Markov chain).The TS-MCMC algorithm starts with a 2K null model.By setting the edge weight of the starting network,selecting the disconnected edge,and restricting the new edge by Tabu search,it solves the problem that the existing algorithm can not reach the goal of the 2.5K null model for high clustering network.The simulation results show that the 2.5K null model generated by TS-MCMC algorithm is closer to the real network than other algorithms,and the accuracy of the 2.5K null model generated by the proposed algorithm is verified.3.Using four real networks: Dolphin,Wiki,Facebook,Microblog to generate null models by random scrambling.The accuracy of the null model is verified by comparing degree distribution,joint degree distribution,average clustering and clustering spectrum.Then through the generated null models,the rumor spread and epidemic spread are studied.The simulation results show that for epidemic propagation: when the network clustering is low and the degree distribution is consistent,the epidemic propagation scale of the final network is almost the same.When the cluster is slightly higher,the two factors of clustering spectrum and joint degree distribution largely affect the final scale of epidemic propagation in the network.For rumor spreading: the final immunization scale of rumors spread is closely related to the infection rate.As the infection rate increases,the rumor spread eventually expands.When the infection rate reaches a certain value,the final spread of the rumor will not change.The larger the clustering coefficient is,the smaller the impact of rumor propagation is.