Construction Of Scientific Collaboration Hypernetwork Model And Its Application

In real life, scientific research personnel can build relationships with coauthors through scientific collaboration, which form a huge network, namely, scientific collaboration network. The network has the characteristics of complex systems, so it can be described quantitatively by the theory of complex network. In a scientific collaboration network, the nodes indicate the authors and the edges indicate the collaborations between the authors, for example, the coauthorship relationships between them. People tend to diffuse knowledge by coauthoring papers in the scientific collaboration systems. However, by means of network science to investigate the knowledge diffusion, one cannot know the information of papers. Therefore,the hypernetwork model based on the hypergraph theory is proposed to study the scientific research cooperation behavior. In this paper, the main work can be divided into the following three aspects.Firstly, we present a local-world non-uniform evolving hypernetwork model, which introduces the hyperedge growth and local-world hyperedge preferential attachment mechanisms. The model takes into account the fact that authors often look for collaborators from their local world and the number of collaborators is always different. At each time step, a newly added hyperedge encircles a new coming node and a number of nodes from a randomly selected local-world. The number of the selected nodes from the local world obeys the uniform distribution and its mean value is m. The analytical and simulation results show that the hyperdegree approximately obeys the power-law form and the exponent of hyperdegree distribution is γ=2 +1 m. Furthermore, we numerically investigate the node degree, hyperedge degree, clustering coefficient as well as the average distance and find that the hypernetwork model shares the scale-free and small-world properties.Secondly, we present a knowledge diffusion model based on the local-world non-uniform evolving hypernetwork, which introduces the preferential diffusion mechanism and the knowledge absorptive capabilityjα, where jα is correlated with the hyperdegree()Hd j of node j. At each time step, we randomly select a node i as the sender, and in probability jp preferentially select a neighbor node j of node i as the recipient, where jp is correlated with the number of cooperation ijC between node i and node j. In the knowledge diffusion process, the node j absorbs part of the knowledge with the knowledge absorptive capabilityjα. Applying the average knowledge stock V(t), the variance 2σ(t) and the variance coefficient c(t) of knowledge stock to measure the growth and diffusion of knowledge, we have made 3 groups of comparative experiments to investigate how different network structures, hypernetwork sizes and knowledge evolution mechanisms affect the knowledge diffusion, respectively. The findings indicate that the hypernetwork is more conductive to promote the knowledge diffusion.Finally, by introducing the Cobb-Douglas production function to the knowledge generation process, we present two dynamic evolution hypernetwork models based on the knowledge creation process. The first model named “HDPH model” adopts the hyperedge growth and the hyperdegree preferential attachment mechanisms. The second model named “KSPH model” adopts the hyperedge growth and the knowledge stock preferential attachment mechanisms. We investigate the effect of the parameters(α, β) of the knowledge production function on the total knowledge stock of the two models. The findings indicate that the total knowledge stock of the two models will become larger as α or β increases. The hyperdegree distribution of HDPH model can be theoretically analyzed by the mean-field theory. The analytic result indicates that the hyperdegree distribution of HDPH model obeys the power-law distribution and the exponent is γ = 2+1/m. Not all knowledge-stock distributions for(α, β) values of HDPH model exhibit a power-law form. While, all knowledge-stock distributions for(α, β) values of KSPH exhibit a power-law form.