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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 FROM AUTHOR]

Bipartite projections have become a common way to measure spatial networks. They are now used in many subfields of geography, and are among the most common ways to measure the world city network, where intercity links are inferred from firm co‐location patterns. Bipartite projections are attractive because a network can be indirectly inferred from readily available data. However, spatial bipartite projections are difficult to analyze because the links in these networks are weighted, and larger weights do not necessarily indicate stronger or more important connections. Methods for extracting the backbone of bipartite projections offer a solution by using statistical models for identifying the links that have statistically significant weights. In this article, we introduce the open‐source backboneR package, which implements several backbone models, and demonstrate its key features by using it to measure a world city network. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Projections of bipartite or two-mode networks capture co-occurrences, and are used in diverse fields (e.g., ecology, economics, bibliometrics, politics) to represent unipartite networks. A key challenge in analyzing such networks is determining whether an observed number of co-occurrences between two nodes is significant, and therefore whether an edge exists between them. One approach, the fixed degree sequence model (FDSM), evaluates the significance of an edge's weight by comparison to a null model in which the degree sequences of the original bipartite network are fixed. Although the FDSM is an intuitive null model, it is computationally expensive because it requires Monte Carlo simulation to estimate each edge's p value, and therefore is impractical for large projections. In this paper, we explore four potential alternatives to FDSM: fixed fill model, fixed row model, fixed column model, and stochastic degree sequence model (SDSM). We compare these models to FDSM in terms of accuracy, speed, statistical power, similarity, and ability to recover known communities. We find that the computationally-fast SDSM offers a statistically conservative but close approximation of the computationally-impractical FDSM under a wide range of conditions, and that it correctly recovers a known community structure even when the signal is weak. Therefore, although each backbone model may have particular applications, we recommend SDSM for extracting the backbone of bipartite projections when FDSM is impractical. [ABSTRACT FROM AUTHOR]

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 114th session of the United States Senate to demonstrate its functionality. [ABSTRACT FROM AUTHOR]