  Network science is a powerful tool for analyzing complex systems in fields
ranging from sociology to engineering to biology. This paper is focused on
generative models of large-scale bipartite graphs, also known as two-way graphs
or two-mode networks. We propose two generative models that can be easily tuned
to reproduce the characteristics of real-world networks, not just
qualitatively, but quantitatively. The characteristics we consider are the
degree distributions and the metamorphosis coefficient. The metamorphosis
coefficient, a bipartite analogue of the clustering coefficient, is the
proportion of length-three paths that participate in length-four cycles. Having
a high metamorphosis coefficient is a necessary condition for close-knit
community structure. We define edge, node, and degreewise metamorphosis
coefficients, enabling a more detailed understanding of the bipartite
connectivity that is not explained by degree distribution alone. Our first
model, bipartite Chung-Lu (CL), is able to reproduce real-world degree
distributions, and our second model, bipartite block two-level Erd\"os-R\'enyi
(BTER), reproduces both the degree distributions as well as the degreewise
metamorphosis coefficients. We demonstrate the effectiveness of these models on
several real-world data sets.

Social and Information Networks;Physics and Society