Generating bipartite networks with a prescribed joint degree distribution

Abstract

Abstract We describe a class of new algorithms to construct bipartite networks that preserves a prescribed degree and joint-degree (degree–degree) distribution of the nodes. Bipartite networks are graphs that can represent real-world interactions between two disjoint sets, such as actor–movie networks, author–article networks, co-occurrence networks and heterosexual partnership networks. Often there is a strong correlation between the degree of a node and the degrees of the neighbours of that node that must be preserved when generating a network that reflects the structure of the underling system. Our bipartite $2K$ ($B2K$) algorithms generate an ensemble of networks that preserve prescribed degree sequences for the two disjoint set of nodes in the bipartite network, and the joint-degree distribution that is the distribution of the degrees of all neighbours of nodes with the same degree. We illustrate the effectiveness of the algorithms on a romance network using the NetworkX software environment to compare other properties of a target network that are not directly enforced by the $B2K$ algorithms. We observe that when average degree of nodes is low, as is the case for romance and heterosexual partnership networks, then the $B2K$ networks tend to preserve additional properties, such as the cluster coefficients, than algorithms that do not preserve the joint-degree distribution of the original network.