Some collaboration-competition bipartite networks

TL;DR

This paper studies collaboration-competition bipartite networks, introducing node weight as a measure, and finds that their distributions follow a shifted power law across diverse real-world systems, suggesting a universal evolution rule.

Contribution

It defines node weights in bipartite networks and demonstrates their distributions follow a shifted power law across various systems, indicating a potential universal evolution pattern.

Findings

Node weight distributions follow a shifted power law.

Universal pattern observed across diverse systems.

Provides a basis for further study of system evolution dynamics.

Abstract

Recently, we introduced a quantity, "node weight", to describe the collaboration sharing or competition gain of the elements in the collaboration-competition networks, which can be well described by bipartite graphs. We find that the node weight distributions of all the networks follow the so-called "shifted power law (SPL)". The common distribution function may indicate that the evolution of the collaboration and competition in very different systems obeys a general rule. In order to set up a base of the further investigations on the universal system evolution dynamics, we now present the definition of the networks and their node weights, the node weight distributions, as well as the evolution durations of 15 real world collaboration-competition systems which are belonging to diverse fields.