On Some Problems Of Diffusion And Transmission In Complex Networks

Spurred by the development of information technology and the advance of social civilization, more and more large-scale information networks emerge. Typical exam-ples include AS-level and router-level topological networks of the Internet, peer-to-peer overlay networks, and online social networks in the World Wide Web. As the networks are closely related to our daily life, it is of utmost importance to search proper methods to characterize basic properties and the evolution of a network's structure, to understand the interplay between the structure and the function of a network. Actually, since 1998 a number of empirical studies have shown that most large-scale networks have some common topological properties, such as the well-known'small-world'effect, scale-freeness, modularity, etc. The kinds of large-scale networks are called roughly'complex networks'. In contrast to simple and small networks, complex network is a very chal-lenging object for research, which attracts more and more attention of interdisplinary researchers recently.Diffusion and transmission are two important processes taking place in various information networks, such as transmission of packets among ASs or routers in the Internet, diffusion of news, public events or sentiment as well as experience in online social networks, and so on. An important and interesting question is:how does the underlying network structure affect the diffusion and transmission of information on a network? That is the subjectâ… studied in the thesis. Detailedly, the contents and main results of the thesis are summarized as follows.1. I have studied the diffusion on weighted scale-free networks and found that the large dispersion of edges weights induce slow diffusion, and the velocity of the diffusion decays in a power-law form after its peak value (SI model). Besides, my results also show that one can restore the diffusion threshold by redistributing or balancing the asymmetric weights of edges (SIS model).2. I have studied the SIRS diffusion on scale-free networks with communities and found that there exists a critical value of the modularity which separates the global diffusion-induced synchronous phase and asynchronous phase, and the intra-community synchronization is weak while the modularity equals one medium value.3. I have analyzed the synchronization phenomena on networks from a view point of diffusion and found a relationship between the synchronizing performance, including synchronizing speed and time-delay tolerance, and the Laplacian eigenvalues of the network. Furthermore, I found that proper time-delay can improve the synchronizing speed.4. Based on the reverse effects of diffusion on network structural evolution, I have thereby proposed an evolutionary model for weighted complex networks. This model can generate weighted scale-free networks with power-law node-degree distribution, power-law node-strength distribution, power-law edge-weight distribution, assortativ-ity, nonlinear degree-strength relation and large clustering coefficient, which were dis-covered widely in real-world information networks.5. I have also proposed an efficient routing strategy which, comparing with the traditional shortest path routing, can improve the transmission capacity and thus can reduce the congestion of scale-free networks in general. The results in the thesis contribute to a better understanding of information diffu-sion and transmission on real-world large-scale networks.