Modeling The Weighted Local-world Networks And Study The Behavior Of Its Applications

Recently,complex networks attract more and more attentions from various fields ofscience and engineering and has become a hot Researching spot. Complex networks describe a wide range of systems in nature and society, such as food web,the networks of scientific communication and the Internet. The global link attachment mechanism and unweighted network models studied in many existing literatures are simplified modeling of real networks.While traditionally these systems have been modeled as binary network,while in a binary network, the edges only represents the presence or absence of interaction,with link weights among their vertex s being either 1 or 0.But many real-world networks are weighted networks with different weights in different links and with local link attachment mechanism.So,based on the topology,the weight and local link preferential attachment mechanism to be introducd, which more in keeping with reality and which is also a forward direction in the complex network researching.Research in this paper focus on the statistical features of the local-world and weighted scale-free networks whose local link preferential attachment mechanism and weight is introduced based on the topology of the global and unweighted scale-free networks.These features include vertex strengths and its distribution,link weights and its distribution,average distance,clustering coefficient and so on, which have been studied by computer simulation.Several aspects of work mainly to be done are as follows:1. It is discovered that there are two inportant characters, local-world character and weighted driven character, in many real-life complex networks. Motivated by this fact, a weight driven local-world network model is proposed, which incorporates the weight dynamicsand the fixed local-world property. By means of mathematical analysis and numerical simulation, the strength distribution of the network model has been obtained. The results are applied to epidemic spreading theory.2. The problem of epidemic spreading has always been concerned by many scientists all over the world. owever, there are seldom studies in the field of weighted local-world network. Since a lot of the real-world networks are weighted, the virus spreading in weighted Local-world complex networks is studied in this paper. With the SI model of virus spreading being adopted and the virus spreading speed between any two nodes being positive correlation with the corresponding weight between them, the effect of different weight distributions on the spreading behavior in three weighted evolving networks is investigated. Study shows that scale-free and Weighted Local-world properites of Weighted Local-world network both have an great effect on the Epidemic Spreading.3. The traditional immunization behavior achieved by deleting all the links adjacent to the epidemic nodes, this behavior lead to reduce the network efficiency. In order to avoid such faultiness, in this paper, we define the weakened immunization in weighted network by reducing the link weight, and meanwhile holding the efficiency of network; Second, a density of infect nodes is obtained by calculating process based on weighted susceptible-infected (SI) epidemic model, the efficiency of networks on weighted networks is defined too; Last, numerical simulations shown that the weakened immunization in weighted network can effectively keep down epidemic spreading and preserve necessary efficiency at same time, which fit well with theoretical analysis in our model.