The backbone of bipartite projections: Inferring relationships from co-authorship, co-sponsorship, co-attendance and other co-behaviors

• Review of methods for extracting the backbone of bipartite projections.
• Demonstration of the stochastic degree sequence model for backbone extraction.
• Identification of political alliances and antagonisms in the U.S. Senate from bill sponsorship data.

The analysis and visualization of weighted networks pose many challenges, which have led to the development of techniques for extracting the network's backbone, a subgraph composed of only the most significant edges. Weighted edges are particularly common in bipartite projections (e.g. networks of co-authorship, co-attendance, co-sponsorship), which are often used as proxies for one-mode networks where direct measurement is impractical or impossible (e.g. networks of collaboration, friendship, alliance). However, extracting the backbone of bipartite projections requires special care. This paper reviews existing methods for extracting the backbone from bipartite projections, and proposes a new method that aims to overcome their limitations. The stochastic degree sequence model (SDSM) involves the construction of empirical edge weight distributions from random bipartite networks with stochastic marginals, and is demonstrated using data on bill sponsorship in the 108th U.S. Senate. The extracted backbone's validity as a network reflecting political alliances and antagonisms is established through comparisons with data on political party affiliations and political ideologies, which offer an empirical ground-truth. The projection and backbone extraction methods discussed in this paper can be performed using the -onemode- command in Stata.