  Bipartite networks are a natural representation of the interactions between
entities from two different types. The organization (or topology) of such
networks gives insight to understand the systems they describe as a whole.
Here, we rely on motifs which provide a meso-scale description of the topology.
Moreover, we consider the bipartite expected degree distribution (B-EDD) model
which accounts for both the density of the network and possible imbalances
between the degrees of the nodes. Under the B-EDD model, we prove the
asymptotic normality of the count of any given motif, considering sparsity
conditions. We also provide close-form expressions for the mean and the
variance of this count. This allows to avoid computationally prohibitive
resampling procedures. Based on these results, we define a goodness-of-fit test
for the B-EDD model and propose a family of tests for network comparisons. We
assess the asymptotic normality of the test statistics and the power of the
proposed tests on synthetic experiments and illustrate their use on ecological
data sets.
