Some Common Properties of Affiliation Bipartite Cooperation-Competition Networks

This article presents a brief review about some common properties of cooperation-competition networks described by affiliation bipartite graphs. Firstly, the distributions of three statistical quantities, the two bipartite graph degrees and a projected unipartite graph degree, which describes the network cooperation-competition configuration, are introduced. The common function forms of the distributions are deduced by the analytic and numerical analyses of a network evolution model, and then verified by the empirical investigations on 23 real world cooperation-competition systems. Secondly, for a description on the competition results, a node weight is proposed which represents a kind of its competition gain. A common node weight distribution function is empirically observed in the 23 real world systems. Thirdly, the relationships between the properties describing the cooperation-competition configuration and the competition properties are discussed. The only example reported in this article is the correlation between the node weight and a bipartite graph degree. These studies may be helpful for the development of complex system theory and the understanding of some important real world systems.