Node Weight Distribution and Disparity of Some Collaboration--Competition Networks

We present an empirical investigation of 14 real world networks, which can be described by bipartite graphs. We show that the basic elements (the actor nodes) in all the networks cooperate and compete in some acts (activities, organizations, or events). Each node is assigned by a `node weight', which denotes the obtained competition result. We are interested in the distribution and disparity of the node weight and propose three parameters for the description. Firstly, empirically we observe that the total node weight distributions of all the systems may be fitted by the so-called `shifted power law' function form. The key parameters of the function, α and γ, can be used to describe the disparity. Secondly, a `node weight disparity', Y, is defined for the same purpose. The empirical relationships among the parameters Y, α and γ, are obtained. From the relationships between Y and α as well as Y and γ, one can deduce the relationship between α and γ, which is in a good agreement with the empirically obtained relationship. The results show that the node weight distribution is very uneven.