Research And Application On Structure Of Collaboration Network Model

Many real systems can be described by complex networks in which a noderepresents the system’s elementary unit, and an edge represents the interaction orrelationship between a pair of nodes. Social network is a kind of important complexnetwork, including one-mode network and two-mode network. In one-mode network,it only contains one kind of nodes, called participant nodes; while two-mode networkcontains two different types of nodes. One kind of the most important networks intwo-mode networks is called as affiliation network. It can be represented as a bipartitegraph with two types of nodes. It generally contains “project” and “participant”denoted by two disjoint node sets, and the relationships between projects andparticipants are usually represented as edges respectively.In recent years, the collaboration network in affiliation networks has gained muchattention from many researchers. In collaboration network, the edges between any twonodes only respect the cooperation relations between nodes, ignoring other relationsbetween nodes, such as competition, dominance and so on. Although collaborationnetwork is represented as a bipartite graph, the one-mode projections of these bipartitegraphs are empirically studied. In these projections, the project nodes are excluded,and the participants that collaborate in a common project are connected by edges.Each project is represented as a complete graph, and the entire one-mode networkbecome a set of complete graphs.We firstly summary some basic knowledge of collaboration network, including theresearching background and researching significance of collaboration networks,several important statistical parameters of describing collaboration network topology and the solving methods for these parameters. Then the collaboration network RDPmodel is studied. We translate the two-mode RDP model that is a bipartite graph toone-mode RDP model that is the one-mode projection of the bipartite graph. Byrate-equation approach, master-equation approach and mean-field approach, weresearch the structural properties of one-mode RDP model, including nodes degreedistribution, joint degree distribution, nodes degree correlation and clusteringcoefficient, and make some numerical simulations by Matlab. Considering thecompetitive aspect among nodes in the evolution process of collaboration network, wepropose the one-mode RDP model based on fitness-driven preferential attachment. Wecall this model one-mode RDP model with fitness. We research the nodes degreedistribution of one-mode RDP model with fitness. Finally, we makes a statistics onscientific collaboration network, according to the papers published in ‘Journal ofIndustrial Engineering and Engineering Management’from Jan2009to Jan2014. Theconcrete research content of this paper is as follows:(1) We introduce the researching background and researching significance ofcollaboration networks, and describe our main work in detail. We firstly summarysome basic knowledge of collaboration network, including some importantcharacteristic parameters that can describe structural properties of collaborationnetwork, including nodes degree distribution, nodes degree correlation, clusteringcoefficient, average path length and so on. Then we present some methods forresearching the important characteristic parameters, including the dynamic methodsthat are rate-equation approach and mean-field approach, as well as the probabilitymethods that are master-equation approach. Finally, we compare and analyze theseapproaches.(2) We referee the two-mode collaboration network model (RDP), and translate itinto one-mode RDP model. By rate-equation approach and master-equation approach，we study the node degree distribution in the one-mode RDP model (RDP) withnumerical simulations verifying the feasibility of the model. It is proved that the nodedegree distribution of the model is a right-skewed power-law like distribution with theexponent γ in interval (1,3]. Using rate-equation approach, master-equation approach and mean-field approach respectively, it all can be proved that the node degreedistribution is approximately power-law distribution for the large enough node degreek. The joint degree distribution are also got by utilizing rate-equation approach andthe node degree distribution. Through the joint degree distribution, we find that thecorrelation relationship of node degrees is nontrivial correlation relationship amongthe degrees of connected nodes that formed by spontaneously. Finally we get theclustering coefficient of the RDP model by calculating the mathematical expectationof degree distribution.(3) We improve the one-mode RDP model for the competitive evolving networkand add the node’s fitness η into the preferential attachment. Then the one-mode RDPmodel based on fitness-driven preferential attachment is proposed. We call this modelone-mode RDP model with fitness. We discover that the fitter nodes can acquire moreconnectivity and the dynamic exponent depends on the fitness η. By calculating thedynamic exponent α(η), a general expression for the node degree distribution ofone-mode RDP model with fitness is acquired. Given the fitness distribution ρ(η), theexplicit form of the node degree distribution can also be obtained. The analysispredictions are found to be in good agreement with the experimental results derivedby numerical simulations.(4) This paper makes a statistics on scientific collaboration network according tothe papers published in ‘Journal of Industrial Engineering and EngineeringManagement’ from Jan2009to Jan2014. The result shows that the scientificcollaboration network is a unconnected network and presents the scale-freecharacteristic. Then we study some related properties of the several larger interiorconnected sub-networks, such as topology structure, clustering coefficient, averagepath and so on. According to the institution and region where scientists work and theresearch field and acquired research achievement of scientists, we find the reason forthe formation of large-scale connected sub-networks. We also analyze the presentsituation of management engineering field and predict the development ofmanagement engineering field in China.The main innovation points are as follows: 1. We translate the two-mode RDP model that is a bipartite graph to one-modeRDP model that is the one-mode projection of the bipartite graph. By rate-equationapproach, master-equation approach and mean-field approach respectively, the nodesdegree distribution expressions of one-mode RDP model are obtained. The jointdegree distribution are got by utilizing rate-equation approach. Through the jointdegree distribution, we find that the correlation relationship of node degrees isnontrivial correlation relationship among the degrees of connected nodes that formedby spontaneously. Finally we get the clustering coefficient of the RDP model bycalculating the mathematical expectation and second moments of degree distribution.2. Considering the competitive aspect among nodes in the evolution process ofcollaboration network, we propose the one-mode RDP model with fitness. The generalexpression for the node degree distribution of one-mode RDP model with fitness isacquired. Given the fitness distribution, the explicit form of the node degreedistribution can also be obtained.3. We makes a statistical analysis on scientific collaboration network, accordingto the papers published in ‘Journal of Industrial Engineering and EngineeringManagement’ from Jan2009to Jan2014.