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1. Illustrating the importance of edge constraints in backbones of bipartite projections

   https://doi.org/10.1371/journal.pone.0302973  

   Neal, Zachary P; Neal, Jennifer Watling (May 2024, PLOS ONE)

   Papadopoulos, Fragkiskos (Ed.)

   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). 

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2. fastball: a fast algorithm to randomly sample bipartite graphs with fixed degree sequences

   https://doi.org/10.1093/comnet/cnac049  

   Godard, Karl; Neal, Zachary P. (December 2022, Journal of Complex Networks)

   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. 

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3. Backbone: An R package for extracting the backbone of bipartite projections

   https://doi.org/10.1371/journal.pone.0244363  

   Domagalski, Rachel; Neal, Zachary P.; Sagan, Bruce (January 2021, PLOS ONE)

   Rozenblat, Celine (Ed.)

   Bipartite projections are used in a wide range of network contexts including politics (bill co-sponsorship), genetics (gene co-expression), economics (executive board co-membership), and innovation (patent co-authorship). However, because bipartite projections are always weighted graphs, which are inherently challenging to analyze and visualize, it is often useful to examine the ‘backbone,’ an unweighted subgraph containing only the most significant edges. In this paper, we introduce the R package backbone for extracting the backbone of weighted bipartite projections, and use bill sponsorship data from the 114 th session of the United States Senate to demonstrate its functionality. 

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4. backbone: An R package to extract network backbones

   https://doi.org/10.1371/journal.pone.0269137  

   Neal, Zachary P. (May 2022, PLOS ONE)

   Cherifi, Hocine (Ed.)

   Networks are useful for representing phenomena in a broad range of domains. Although their ability to represent complexity can be a virtue, it is sometimes useful to focus on a simplified network that contains only the most important edges: the backbone. This paper introduces and demonstrates a substantially expanded version of the backbone package for R, which now provides methods for extracting backbones from weighted networks, weighted bipartite projections, and unweighted networks. For each type of network, fully replicable code is presented first for small toy examples, then for complete empirical examples using transportation, political, and social networks. The paper also demonstrates the implications of several issues of statistical inference that arise in backbone extraction. It concludes by briefly reviewing existing applications of backbone extraction using the backbone package, and future directions for research on network backbone extraction. 

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5. Inferring signed networks from preschoolers’ observed parallel and social play

   https://doi.org/10.1016/j.socnet.2022.07.002  

   Neal, Jennifer Watling; Neal, Zachary P; Durbin, C Emily (October 2022, Social Networks)

   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. 

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