Abstract
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 closed-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.
Highlights
Bipartite interaction networks are used to represent a diverse range of interactions in various fields such as biology, ecology, sociology or economics
A bipartite interaction network can be viewed as a bipartite graph, the nodes of which being individuals pertaining to two different groups, and an edge between two nodes being present if these two individuals interact
We prove the asymptotic normality of the count of any given motif under the bipartite expected degree distribution (B-EDD) model, under sparsity conditions
Summary
Bipartite interaction networks are used to represent a diverse range of interactions in various fields such as biology, ecology, sociology or economics. The B-EDD model can obviously accommodate to the network dimension (number of top and bottom nodes), for its density and for some existing imbalances between the degrees of the nodes Such imbalances play an important role in many fields: in ecology they are related to the opposition between generalist insects (capable of pollinate a large number of plant species) and specialist insects (interacting with a limited number of plant species) (see e.g. Vazquez and Aizen, 2004; Bascompte and J., 2006; Simmons et al, 2019b).
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