Modeling The Directed And Weighted Scale-free Networks And Study The Behavior Of Its Evolution

Recently, complex networks attract more and more attentions from various fields of science 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 unoritented 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 or with different direction in different links.So,based on the topology ,the weight and the direction 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 directed and weighted scale-free networks whose direction and weight is introduced based on the topology of the undirected and unweighted scale-free networks.These features include vertex degrees and its distribution,vertex strengths and its distribution,link weights and its distribution, average distance,clustering coefficient,betweenness centrality ,and so on..Which have been studied by computer simulation.Several aspects of work mainly to be done are as follows.(1) Model the undirected and unweighted network based on the growth and preferential attachment of BA model,observe the behavior of its evolution through the computer simulation ,and prove the degrees distribution of the BA scale-free complex network yields the power-law distribution.(2) Model the undirected and weighted network based on the vertex strengths preferential attachment of BBV model,observe the behavior of its evolution through the computer simulation ,and prove the degrees distribution,vertex strengths distribution and link weights distribution of the BBV scale-free complex network also yields the power-law distribution.And found that adding the weight to the network would make the value of the average distance turn high. (3) On the basis of the above studies,and based on the weighted network as BBV model,model the directed and weighted network whose direction is introduced randomly and observe the behavior of its evolution through computer simulation.We found that the direction being introduced to the network make the distribution of the out/in node degree and the out/in node strength appear a short level distribution at the top before showing the power-law distribution., but the link weight always yields the power-law distribution, and the value of the average clustering coefficient has not been improved.At the last, in order to enhance the value of the clustering coefficient ,we extended the directed and weighted BBV model by improve the linked nodes'election rules-the first edge of the new node according to the node strength preference attachment to link with the old node, the other edges of the new node link firstly with the neighbor nodes of the first selected old node according to the order of the neighbors'node strengths from high to low.If the number of the neighbor nodes is not enough, then , according to the node strength preference attachment to select another old node from the network. The computer simulation result shows that the extended model has the feature of high clustering coefficient.