Self-organization of collaboration networks

José J. Ramasco1, S. N. Dorogovtsev2,3,4 and Romualdo Pastor-Satorras5
1Centro de Física do Porto and Departamento de Física, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal.
2Departamento de Física, Universidade de Aveiro, Campus Universitario de Santiago, 3810-193 Aveiro, Portugal.
2Laboratory of Physics Helsinki University of Technology FIN-02015 HUT, Finland.
4A. F. Ioffe Physico-Technical Institute, 194021 St. Petersburg, Russia.
5Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord, 08034 Barcelona, Spain.

(March 2004)

We study collaboration networks in terms of evolving, self-organizing bipartite graph models. We propose a model of a growing network, which combines preferential edge attachment with the bipartite structure, generic for collaboration networks. The model depends exclusively on basic properties of the network, such as the total number of collaborators and acts of collaboration, the mean size of collaborations, etc. The simplest model defined within this framework already allows us to describe many of the main topological characteristics (degree distribution, clustering coefficient, etc.) of one-mode projections of several real collaboration networks, without parameter fitting. We explain the observed dependence of the local clustering on degree and the degree--degree correlations in terms of the ``aging'' of collaborators and their physical impossibility to participate in an unlimited number of collaborations.