Understanding how both the partitions of a bipartite network affect its one-mode projection

It is a well-known fact that the degree distribution (DD) of the nodes in a partition of a bipartite network influences the DD of its one-mode projection on that partition. However, there are no studies exploring the effect of the DD of the other partition on the one-mode projection. In this article, we show that the DD of the other partition, in fact, has a very strong influence on the DD of the one-mode projection. We establish this fact by deriving the exact or approximate closed-forms of the DD of the one-mode projection through the application of generating function formalism followed by the method of iterative convolution. The results are cross-validated through appropriate simulations.

[1]  Niloy Ganguly,et al.  Modeling discrete combinatorial systems as alphabetic bipartite networks: theory and applications. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Marta C. González,et al.  Cycles and clustering in bipartite networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  D. Owen.  Handbook of Mathematical Functions with Formulas , 1965 .

[4]  Niloy Ganguly,et al.  Emergence of a non-scaling degree distribution in bipartite networks: A numerical and analytical study , 2007 .

[5]  Petter Holme,et al.  Network bipartivity. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  M E Newman,et al.  Scientific collaboration networks. I. Network construction and fundamental results. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  M Ausloos,et al.  Uncovering collective listening habits and music genres in bipartite networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[9]  S. Pinker.  The language instinct : how the mind creates language , 1995 .

[10]  J. A. Rodríguez-Velázquez,et al.  Spectral measures of bipartivity in complex networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  S. N. Dorogovtsev,et al.  Self-organization of collaboration networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  S. Pinker,et al.  The Language Instinct: How the Mind Creates Language , 1994 .

[13]  Jean-Loup Guillaume,et al.  Bipartite graphs as models of complex networks , 2006 .

[14]  Jean-Loup Guillaume,et al.  Bipartite structure of all complex networks , 2004, Inf. Process. Lett..

[15]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[16]  T S Evans,et al.  Exact solution for the time evolution of network rewiring models. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.