Spreading Dynamics On The Popularity-and-Similarity Based Networks

The spreading of the epidemic in human society,the spreading of computer viruses on the Internet,and the spreading of fake news in social networks are important research topics in complex networks.Therefore,it is of great significance to investigate the influence of network structure on the spreading processes and the interactions between them,which contribute to the control of the spreading of epidemic,computer viruses,and fake news.This dissertation mainly focuses on three issues: the modeling and dynamic analysis of epidemic spreading on the networks based on the popularity-and-similarity algorithm,the modeling and dynamic analysis of fake news spreading on the networks based on the popularity-and-similarity algorithm,and the influence of geometric correlations on the epidemic and fake news spreading in multiplex networks.By adopting the mean-field theory,ordinary differential and partial differential equations modeling,nonlinear stability analysis method,and the Monte-Carlo method,this dissertation establishes epidemic spreading models and fake news spreading models on the networks based on the popularity-and-similarity algorithm.The main contributions of the dissertation are as follows:(1)Two epidemic spreading models are proposed with consideration of the popularity of nodes,called r-SI and r-SIS,respectively,which describe the epidemic processes on the network based on the popularity-and-similarity algorithm.The proposed models are spatio-temporal epidemic models and expressed as partial differential equations,in which the infection density function is expressed as a function of both the popularity of nodes and time.The numbers of equations do not change even if the scales of the networks become larger.Simulations are performed on both artificial and real networks,demonstrating the effectiveness of the proposed models.Moreover,the infection density increases nonlinearly with the increase of the popularity of nodes.(2)A fake news spreading model is proposed with similarity taken into account,assuming that the similarity between individuals can affect the transmission rate.The model describes the fake news spreading processes on the networks based on the popularity-and-similarity algorithm.Simulations show that the similarity of two connected nodes and the product of their degrees are positively correlated when the network temperature is small,and the similarity of two connected nodes decreases as the product of their degrees increases.Therefore,the similarity between individuals is described as the function of the products of their degrees.The critical threshold and maximum spreading are obtained by theoretical analysis.The critical threshold is directly proportional to the similarity function and in inverse proportion to the influence coefficient.(3)An individual-based mean-field model for fake news spreading is proposed with consideration of the similarity between individuals,which describes the fake news spreading processes on the networks based on the popularity-and-similarity algorithm.Both the theoretical analysis and Monte-Carlo simulations show that the critical threshold is in inverse proportion to both the maximum eigenvalue of the angular matrix and the influence coefficient.(4)The influence of the geometric correlations on the epidemic spreading on multiplex networks is investigated.The simulations on both the artificial networks and real-world networks show that radial correlations and\or the angular correlations reduce the epidemic threshold and lead to a smaller scale of the outbreak.Moreover,although geometric correlations and overlapped links are positively correlated,the influence of geometric correlations on epidemic spreading cannot be replaced by overlapped links.(5)The spreading of fake news in multiplex social networks is investigated by combining the geometric correlations between layers.The results show that the spreading speed and the final scale of fake news in multiplex networks are larger than that of single-layer networks,and the fake news is more likely to break out in multiplex networks.The spreading processes of fake news in the multiplex networks are compared with that in the reconstructed networks.The results show that the spreading speed and the final scale of fake news in the reconstructed network are larger than that in the original networks,and the fake news is more likely to break out in the reconstructed network.