Competition and fitness in one-mode collaboration network

• Reveal the competitive aspect of collaboration network.
• One-mode RDP model with fitness is proposed.
• General expression for degree distribution of the proposed model is obtained.
• Given fitness distribution, explicit form for degree distribution is acquired.

The fitness to compete for links is a very critical factor to decide the rate that nodes increase their connectivity in a network. In this paper, the node degree distribution of one-mode collaboration model (one-mode RDP model) is researched by mean-field approach and we obtain the node degree distribution of this model is a power-law distribution for large enough node degree k  . Some numerical simulations are made to verify the feasibility of the node degree distribution for this model. Then we improve the one-mode RDP model for the competitive evolving network and come up with a model that is one-mode RDP model based on fitness-driven preferential attachment (we call this model one-mode RDP model with fitness). We discover that the fitter nodes can acquire more connectivity and the dynamic exponent depends on the fitness ηη. By calculating the dynamic exponent α(η)α(η), a general expression for the node degree distribution of one-mode RDP network with fitness is acquired. Given the fitness distribution ρ(η)ρ(η), the explicit form of the node degree distribution can also be obtained. The analytical predictions are found to be in good agreement with the experimental results derived by numerical simulations.