Analysis Of Spreading Dynamics Of Epidemic And Information In Complex Networks

Complex networks, composed of a large number of nodes and interactions between nodes, have very complicated topology. They exist extensively in the nature and the real world, such as communication networks, social networks and biological networks. Researchers have built various models of complex networks from different disciplines and fields, and analyzed their topology. They have also investigated the relation between topology of these models and func-tions and characteristics of networks. All kinds of spreading processes appear to be universal in complex networks and deeply influence people’s production and living. Therefore, the rel-ative research on spreading dynamics on complex networks has become a hot topic in recent years. In this study, we make a deep research on spread of epidemic and information in complex networks. Main innovations of this paper are as follows:(1) Homogeneity of epidemic spreading in complex networks is investigated. In order to obtain analytical solution, researchers often adopt the homogeneous mixing hypothesis, that is, epidemic distribution is homogeneous in a system. However, as infected individuals always infect their neighbors, the homogeneous mixing hypothesis is dubious and need to be verified by experiments. So, the characteristic infected cluster size is introduced to analyze homogeneity of epidemic spreading in static and dynamic complex networks. Simulation results show that infected individuals always prone to gather into large clusters, thus they are always distributed inhomogeneously. Furthermore, we find that the moving speed of individuals v has important effects on homogeneity of epidemic distribution, that is, when v is smaller, epidemic distribution is more inhomogeneous; when v is large, epidemic distribution is almost homogeneous;(2) Correlation dimension of complex networks is defined and calculated. In a series of papers published in Nature and other journals, Song et al. suspected that complex networks have fractal features and self-similar structure, and proposed a method calculating fractal di-mension of complex networks, i.e., the box-counting algorithm. Process of figuring out the minimum number of boxes needed to cover the entire network is an NP (non-deterministic poly-nomial) hard problem, so they linked this to graph coloring problem and proposed optimized box-counting algorithms. They believed that it’s impossible to significantly improve the calcu-lation speed of fractal dimension with no significant loss of accuracy. We generalize correlation dimension describing geometric objects in Euclidean space to complex networks based on topol-ogy, and accordingly analyze fractal structure of complex networks. We further verify that some complex networks have self-similar structure, and obtain their correlation dimensions. The time complexity of correlation dimension algorithm is O(N2.376ln N)(N is node number), which is much better than exponential time of Song et al.’s algorithm. It’s worth mentioning that, on the very day that our results about correlation dimension of complex networks were published, Lacasa et al. proposed a similar definition of correlation dimension in Physical Review Letters, and obtained correlation dimension similar to our work by traversing the network.(3) An algorithm for building hierarchical and modular complex networks is proposed based on a complete binary tree. Starting with a complete binary tree, and considering that spreading always occurs among nearby individuals with a greater probability and occurs among remote individuals with a lower probability in the real world, our algorithm builds networks by adding links to the complete binary tree with different probabilities according to topological distance between nodes. Simulation results show that, the clustering function C(k) of complex networks built with the proposed algorithm satisfies C(k)∝k-β and their clustering coefficients are independent of their network sizes. This means that these networks have hierarchical and modular structure. The correlation dimension algorithm is applied to these networks, and simu-lation results indicate that these networks have self-similarity.(4) Two new dynamic network models are proposed based on random walk and informa-tion spread. In the first model, two information with the same priority spreads among random walking individuals. As individuals move, each one remembers the information carried by most of its neighbors. In this way, two information competes with each other. We find that, the mov-ing speed of individuals decides the competition, that is, two information always coexist in the static case, and only one information eventually remains in the dynamic case. We also explain the reasons for the phenomenon. The second model studies the influence of information spread on individual movement of a flock in a closed cell. Our research shows that, as long as indi-viduals generate and timely transmit corresponding information when reaching boundaries, and align with their neighbors when moving away from the boundaries, they can move along the long side of the cell. We further investigate the effects of system parameters on turning time of flock and formation of single cluster.