Research On Weighted Multi-Local Network Based On Bidirectional Preferential Attachment Mechanism

Recently, complex networks attract more and more attentions from various fieldsof science and engineering and has become a hot researching spot. Many systems innature and social life can be described by the complex networks, such as the foodchain network, scientists cooperation network and the Internet. The development ofcomplex networks caused the revival of network modeling. Researchers try toestablishment models which match to the real networks to imitate the properties of thereal networks. The BA model used the degree preferential attachment mechanism toimitate binary networks. But many real networks seem not to be governed by theglobal preferential attachment mechanism. Therefore the local link attachmentmechanism may be more suitable for many networks, research on local-worldnetworks will help us better understand the reality of more complex networks. In thestudy of local-world networks, many researchers focused on binary networks, butmany individuals have large differences between the strength and density, thusconsider the weight of the network can descript the actual system in detail. So, basedon the topology, the weight and local link preferential attachment mechanism to beintroduced, which more in keeping with reality and which is also a forward directionin the complex network researching.Research in this paper focus on the statistical features of the local-world andweighted scale-free networks whose local link preferential attachment mechanism andweight is introduced based on the topology of the global and unweighted scale-freenetworks．These features include vertex strengths and its distribution, link weights andits distribution, average distance, clustering coefficient and so on, which have beenstudied by computer simulation. Several aspects of work mainly to be done are asfollows:1. Research in this paper focus on the statistical features of the local-world andweighted scale-free networks and especially in the inspired of the multi-local-world model, we propose a weighted multi-local-world network model based on bidirectionalpreferential attachment mechanism. In this model the growth dynamics of the networkis not only involved in addition new local worlds, new nodes, adding links, deletion ofold links and old nodes, but also involved the weights dynamic process of the network.After that we provide a detailed analytical and numerical inspection of the model andfind that the strength of the model displays good right-skewed distribution character.Change the value of the parameter, the evolution results of the network whichadvanced under different rules obeys the power-law distribution too.2. According to the data collected from the real database to build real cooperationnetwork, comparative analysis of the statistical characteristics of model that the paperconstructed and the real cooperation network, found that the newly constructednetwork model is more in line with the actual networks.3. The problem of rumor spreading has always been concerned by many scientistsall over the world. Since a lot of the real-world networks are weighted, the rumorspreading in the new model that we proposed in previous is studied in this paper. Withthe SIR model of rumor spreading being adopted and the rumor spreading speedbetween any two nodes being positive correlation with the corresponding weightbetween them. Study shows that scale-free and weighted local-world properties ofweighted local-world network both have a great effect on the rumor spreading.4. Researchers gradually discovered an important property of complex networkswhich is community structure. Detecting community structure of complex networkscontributes to analyze the topology structure and characteristic of complex networks,also to understand the functions of them and can found the hidden disciplines ofcomplex networks and forecast the behaviors of them. We use nonnegative matrixfactorization to detect communities in the weighted local-world network that weproposed, and experimental results show the significance of the proposed approach.