Research On The Modeling And Spreading Dynamics Of Complex Networks

Many complex systems in real world can be described by complex networks made up of interactive individuals, discoveries of the small-world effect and scale-free property make complex network becoming one of the most rapidly developing areas. At present,complex network has already become an essential tool for us to understand complex systems. On the one hand, the study of complex networks is helpful for us to find out the structural properties of the real networks and their formation mechanism. On the other hand, it is useful for us to recognize the dynamical process in the complex networks,which is of great importance for us to optimize and control the dynamic process in real networks.In this thesis, we concentrate on the network evolution and spreading dynamics of complex networks, main points and innovations of this thesis are as follows:We propose a network evolution model based on the common-neighborhood driven mechanism. After extensive study on the small-world and scale-free properties of networks, the research focus is shifting to detailed local structures. Empirical analysis shows that many real networks exhibit the power-law clique-degree distribution, and the distribution exponents decrease with the increase of the order of the clique. This general regularity cannot be produced by the rich-get-richer mechanism. The proposed commonneighbor-driven model well reproduces the observed power-law clique-degree distribution, which indicates that the common-neighborhood-driven mechanism is an essential factor leading to the emergence of local structures.We propose a directed network evolution model for online social network, which reproduces the empirical result for the mesoscale structures, and study the interaction between structures at different scales. Empirical results show that not only the local structures given by the indegree, outdegree, and reciprocal degree distributions follow a similar scaling behavior, the mesoscale structures represented by the distributions of close-knit friendship structures also exhibit a similar scaling law. We propose a simple directed network model that incorporates reciprocation mechanism and preferential attachment mechanism and captures the observed properties. Through rate equation analysis, we find that in the local-scale, the same scaling behavior of indegree and outdegree distributions stems from indegree and outdegree of nodes both growing as the same function of the introduction time, and the reciprocal degree distribution also shows the same power-law due to the linear ralationship between the reciprocal degree and in/outdegree of nodes. In the mesoscale, the distributions of four closed triples representing close-knit friendship structures are found to exhibit identical power-laws, a behavior attributed to the negligible degree correlation. Intriguingly, all the power-law exponents of the distributions in the local-scale and mesoscale depend only one global parameter, the mean in/outdegree. This work helps us understand the interplay between structures on different scales in online social networks.We study the properties of components in the random graph with degree-2 nodes and provide an efficient method to generate the random graph with degree-2 nodes. Simulation results shows that there exists giant component in the random graph with degree-2nodes, which indicate that the well-known result is incorrect and the degree-2 nodes play role for the emergence of giant component. Furthermore, we find that the average size of components and giant components are both not dependent on the network size, and component size distribution follows power-law function.We study the impacts of the temporal heterogeneities of human activities on the spreading dynamics. Based on a fully mixed population, we study the influence of the heterogeneous inter-event time on the spreading dynamics. Extensive results shows that the heterogeneity of activities at the population level remarkably accelerates the speed of spreading, while the heterogenous inter-event time at the individual level affect the spreading processes in a more complicated way. Based on the uncorrelated scale-free networks without degree-degree correlation, we study the impact of the heterogenous response time on the spreading dynamics. Simulation results show that the stronger the heterogeneity of response time is, the faster the information spreading is in the early and middle stages. Following a given heterogeneity, the procedure of reducing the correlation between the response times and degrees of individuals can also accelerate the spreading dynamics in the early and middle stages. But, in the late stage, the full prevalence time does not monotonically change with the buildup of the response-time heterogeneity and the reduction of the response time-degree correlation, and there exists an optimal value,respectively.We propose a weighted susceptible-infected-susceptible model and investigate the influence of the weights on spreading dynamics. Based on six realistic networks, we find that the epidemic prevalence can be largely promoted when strong ties are favored.By comparing with two statistical null model, we show that the distribution pattern of weights, rather than the topological structure, mainly contributes to the observations.Further analysis suggests that the weight-weight correlation mainly affects the results.