This paper suggests a self-adaptive bi-particle graph model, which describes the collaboration network between the principal investigators and their assistants. The model considers the choices, strategies, competitions, and the induced evolutions of the principal investigators and their assistants as actors as well as the evolution of the whole network. The simulation results of all the different single-particle graphs obtained by different methods of projection show a good agreement with the statistical data of the collaboration between American mathematicians and neuroscientists during 1991 and 1998 That shows a self-adaptive complex network can selforganize to a small world and scale-free structure. This article also discusses the similarities and differences of the simulation results of the different projected single-particle graphs of the bi-particle graph.