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Abstract Many applications require randomly sampling bipartite graphs with fixed degrees or randomly sampling incidence matrices with fixed row and column sums. Although several sampling algorithms exist, the ‘curveball’ algorithm is the most efficient with an asymptotic time complexity of $O(n~log~n)$ and has been proven to sample uniformly at random. In this article, we introduce the ‘fastball’ algorithm, which adopts a similar approach but has an asymptotic time complexity of $O(n)$. We show that a C$$\texttt{++}$$ implementation of fastball randomly samples large bipartite graphs with fixed degrees faster than curveball, and illustrate the value of this faster algorithm in the context of the fixed degree sequence model for backbone extraction. 

Collecting network data directly from network members can be challenging. One alternative involves inferring a network from observed groups, for example, inferring a network of scientific collaboration from researchers’ observed paper authorships. In this paper, I explore when an unobserved undirected network of interest can accurately be inferred from observed groups. The analysis uses simulations to experimentally manipulate the structure of the unobserved network to be inferred, the number of groups observed, the extent to which the observed groups correspond to cliques in the unobserved network, and the method used to draw inferences. I find that when a small number of groups are observed, an unobserved network can be accurately inferred using a simple unweighted two-mode projection, provided that each group’s membership closely corresponds to a clique in the unobserved network. In contrast, when a large number of groups are observed, an unobserved network can be accurately inferred using a statistical backbone extraction model, even if the groups’ memberships are mostly random. These findings offer guidance for researchers seeking to indirectly measure a network of interest using observations of groups. 

Bipartite projections (e.g., event co-attendance) are often used to measure unipartite networks of interest (e.g., social interaction). Backbone extraction models can be useful for reducing the noise inherent in bipartite projections. However, these models typically assume that the bipartite edges (e.g., who attended which event) are unconstrained, which may not be true in practice (e.g., a person cannot attend an event held prior to their birth). We illustrate the importance of correctly modeling such edge constraints when extracting backbones, using both synthetic data that varies the number and type of constraints, and empirical data on children’s play groups. We find that failing to impose relevant constraints when the data contain constrained edges can result in the extraction of an inaccurate backbone. Therefore, we recommend that when bipartite data contain constrained edges, backbones be extracted using a model such as the Stochastic Degree Sequence Model with Edge Constraints (SDSM-EC). 

Abstract Shared memberships, social statuses, beliefs, and places can facilitate the formation of social ties. Two-mode projections provide a method for transforming two-mode data on individuals’ memberships in such groups into a one-mode network of their possible social ties. In this paper, I explore the opposite process: how social ties can facilitate the formation of groups, and how a two-mode network can be generated from a one-mode network. Drawing on theories of team formation, club joining, and organization recruitment, I propose three models that describe how such groups might emerge from the relationships in a social network. I show that these models can be used to generate two-mode networks that have characteristics commonly observed in empirical two-mode social networks and that they encode features of the one-mode networks from which they were generated. I conclude by discussing these models’ limitations and future directions for theory and methods concerning group formation. 

Early childhood is an important developmental period for network formation. However, the observational methods used for measuring young children’s networks present challenges for capturing both positive and negative ties. To overcome these challenges, we explored the use of a bipartite projection backbone model for inferring both negative and positive ties from observational data of children’s play. Using observational data collected in one 3-year-old (N = 17) and one 4-year-old (N = 18) preschool classroom, we examined whether patterns of homophily, triadic closure, and balance in networks inferred using this method matched theoretical and empirical expectations from the early childhood literature. Consistent with this literature, we found that signed networks inferred using a backbone model exhibited gender homophily in positive ties and gender heterophily in negative ties. Additionally, networks inferred from social play exhibited more closed and balanced triads than networks inferred from parallel play. These findings offer evidence of the validity of bipartite projection backbone models for inferring signed networks from preschoolers’ observed play. 

Abstract Political network data can often be challenging to collect and clean for analysis. This article demonstrates how the incidentally and backbone packages for R can be used together to construct networks among legislators in the US Congress. These networks can be customized to focus on a specific chamber (Senate or House of Representatives), session (2003 to present), legislation type (bills and resolutions), and policy area (32 topics). Four detailed examples with replicable code are presented to illustrate the types of networks and types of insights that can be obtained using these tools.