  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 (FFM), fixed row model (FRM), fixed column model (FCM),
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.
