Structure properties of one-mode collaboration network model based on rate equation approach

• Two-mode collaboration network model (RDP) is translated into one-mode RDP model.
• Node degree distribution is got by rate-equation approach.
• Joint degree distribution is obtained by rate-equation approach.
• Correlation relationship of node degrees is nontrivial correlation relationship.
• Clustering coefficient of the one-mode RDP model is acquired.

The rate equation approach is very useful to describe the dynamic structure property of collaboration network, especially in calculating the node degree distribution and the joint degree distribution, and considering the correlation of node degrees. In this paper, we referee the two-mode collaboration network model (RDP), and translate it into one-mode RDP model. By the rate-equation approach, we study the node degree distribution in the one-mode RDP model (RDP) with numerical simulations verifying the feasibility of the model. It is proved that the node degree distribution of the model is a right-skewed power-law like distribution with the exponent γγ in interval (1,3](1,3]. For the large enough node degree k, it can be proved that the node degree distribution is approximately power-law distribution. The joint degree distribution are also got by utilizing rate-equation approach and the node degree distribution. Through the joint degree distribution, we find that the correlation relationship of node degrees is nontrivial correlation relationship among the degrees of connected nodes that formed by spontaneously. Finally we get the clustering coefficient of the RDP model by calculating the mathematical expectation of degree distribution.