A cooperative game model for the multimodality of coauthorship networks

This study provided a game model to simulate the evolution of coauthorship networks, which is a geometric hypergraph built on a circle. A fraction of nodes are randomly selected to attach an arc to express their reputation. The cooperation condition of a new node and existing nodes depends on their distance and the existing nodes' reputation. The condition gives an expression of kin selection and network reciprocity, two typical mechanisms of cooperation. The size of a node's reputation is expressed by the length of its arc, which is defined by a function of time and hyperdegree. The function describes the heterogeneity in the size of reputation on nodes and that in the fading speed of reputation on hyperdegrees. The model reveals that the heterogeneities can reproduce the dichotomy of node clustering and degree assortativity, as well as the trichotomy of degree and hyperdegree distributions: generalized Poisson, power-law, and exponential cutoff.