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Abstract 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. 

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. 

Children and adolescents interact in peer groups, which are known to influence a range of psychological and behavioral outcomes. In developmental psychology and related disciplines, social cognitive mapping (SCM), as implemented with the SCM 4.0 software, is the most commonly used method for identifying peer groups from peer report data. However, in a series of four studies, we demonstrate that SCM has an unacceptably high risk of false positives. Specifically, we show that SCM will identify peer groups even when applied to random data. We introduce backbone extraction and community detection as one promising alternative to SCM, and offer several recommendations for researchers seeking to identify peer groups from peer report data.