Nonrandom behavior in the projection of random bipartite networks

There are two main categories of networks studied in the complexity physics community: Monopartite and bipartite networks. In this paper, we present a general framework that provides insights into the connection between these two classes. When a random bipartite network is projected into a monopartite network, under quite general conditions, the result is a nonrandom monopartite network, the features of which can be studied analytically. Unlike previous studies in the physics literature on complex networks, which rely on sparse-network approximations, we provide a complete analysis, focusing on the degree distribution and the clustering coefficient. Our findings primarily offer a technical contribution, adding to the current body of literature by enhancing the understanding of bipartite networks within the community of physicists. In addition, our model emphasizes the substantial difference between the information that can be extracted from a network measuring its degree distribution, or using higher-order metrics such as the clustering coefficient. We believe that our results are general and have broad real-world implications.