Generating bipartite networks with a prescribed joint degree distribution

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 neighbors 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 neighbors 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.

Generating a heterosexual bipartite network embedded in social network

“…We introduce an algorithm that embeds a heterosexual network within a social network and matches the sexually active population's joint-degree distribution. The heterosexual network preserves the bipartite joint degree (BJD) distribution matrix that represents the correlations between then number of partners a person has and the number of partners their partners have (Boroojeni et al 2017). The algorithm has three stages:…”

“…We call this reduced social bipartite network as BSocNet. (iii) Generate an embedded heterosexual bipartite network, SexNet: We then use the BSocNet to define a heterosexual network of sexual partnerships, the SexNet, with a prescribed bipartite joint degree matrix BJD based on survey data (Boroojeni et al 2017). That is, we preserve the correlations between the number of partners a person has and the distribution for the number of partners their partners have.…”

“…These graphs must account for the distribution for the number of sexual partners people have (their degree distribution) and the number of partners their partners have (the joint-degree, or degree-degree, distribution). The existing algorithms that generate bipartite random graphs preserving degree and joint-degree distributions of the nodes are strictly based on the number of partners people have and not other demographic factors, such as age or location (Newman 2002;Hakimi 1962;Boroojeni et al 2017;Azizi et al 2016Azizi et al , 2017Azizi et al , 2018.…”

“…Our new network generation approach uses the underlying extended social network of a population to extend these previous algorithms for generating bipartite heterosexual networks with prescribed joint-degree distribution (Boroojeni et al 2017). Many sexual partnerships are formed from within a person's social circle, defined by the people they have regular social contact with and the contacts of their contacts (their extended social network).…”

Using an agent-based sexual-network model to guide mitigation efforts for controlling chlamydia

“…The fraction of men with i partners is the sum of the i th row divided by i, and the fraction of women with j partners is the sum of the j th column divided by value j. The algorithm in [31] guarantees that the joint-degree distribution of generated network is consistent with the Kissinger et al Check It study of the behavior of 15 − 25 year-old sexually active African American men and women in New Orleans [11], Table 3. The second most sensitive parameter is the natural recovery period, τ n = 1/γ n .…”