Research On Weighted Local Network And Community Division Algorithm Based On Complex Network

The study of complex systems with complex network theory is the basic consensus of the scientific community, and has been received widespread attention by researchers from various discipline field. Reseach shows that there exists the inherent and intrinsical relation between topological structure and network behavior characteristics of complex systems, and the complex network theory provides the theoretical basis for revealing potential mechanism of complex systems. Therefore, building the reasonable and real complex network model and designing efficient community division algorithm, which is a very important issue in the study of complex networks, can better reflect evolution rule and structural features of real systems and have a more precise understanding of network functionality or predict the future behavior of real systems.The research contents are as follows:Firstly, in order to reveal the law behind the weighted network evolution mechanism and establish the pattern that matches the evolution of systems in the real world more comprehensively, we consider the three major characteristics:local feature, the dynamic connection characteristics inside and outside the local world and the properties of triangle laws, and establish the dynamic local world network model of TF rule embedded mechanism(TF-DLW model). The model is integrated into the TF triangle laws mechanism and BBV weighted dynamic evolution standards during each evolution process. Applying the famous mean field theory put forward by statistical physics, the mathematical theories derivate that the strength distribution of TF-DLW evolution model obey the power law distribution characteristics. The computer simulation experiment of TF-DLW model on degree distribution, strength distribution, edged weight distribution are all found with the obvious power law fat tail phenomenon, the embedded triangle structure enables the model to adjust the scope size of the clustering coefficient more smoothly, and the degree-strength relevance graph shows the linear relationship.Secondly, community structure is the most important structure characteristics in the study of complex network. Recently, different types of partition algorithm have been put forward from different research perspective. Based on the dynamic process, the paper presents a novel method of community structure division, which establishes the close relationship between the mathematical inequalities provided by the formation of the simple community structure and the dynamics model Potts model. From the dynamics perspective, we construct the dynamic iteration system of the membership vector of the nodes. In order to better nodes which are not uniformly distributed, the dynamic equation of nodes membership vector is affected by two latest measure indexes. One indicator is that the weighting parameter W considering the common neighbor ratio and edge-betweenness ratio. Another indicator is concerning the density of nodes distribution, namely the tightness coefficient T. In the next stage, we study a new Improved-EM algorithm based on the properties of dynamics. By dynamic iteration of the algorithm, the objective function’s optimal value can be searched out effectively, and obtain the optimal community structure. Finally, the community structure partitioned by the Improved-EM algorithm is optimized by Stability optimization scheme which can effectively alleviate and optimize the resolution limit problem brought by objective function.Thirdly, simulation experiment mainly focuses on the LFR benchmark network and some data network of real world. In the test of the LFR benchmark network, making a comparative study of several famous partition algorithms on running time, the values of Stability, accuracy and so on, the Improved-EM algorithm are all superior to several other partition algorithms in different ways. During the study process of real-world data, the Zarchary karate club network community, American college football network community detected by Improved-EM algorithm are matching with their original data network community. During the process of studying bottlenose dolphin social network, we build a novel evaluation index which is called as tight similar index TSI. The parameter value, which is higher than the HWI, can be demonstrated to not only better measure the frequency degree for establishing contacts between the dolphins, but also mine the topological structure rules of the dolphins network. Therefore, the TSI provides the reliable reference of the actual data values for testing the dolphins relationship network, and the community structure detected by the algorithm would basis match the original data of the dolphin network.