2021/03/23 by Tâm Le Minh, Minh, Tâm Le · 1 citation
Mathematics · Physics and Astronomy · #Random Matrices and Applications #Complex Network Analysis Techniques #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.2103.12597
Bipartite networks with exchangeable nodes can be represented by row-column exchangeable matrices. A quadruplet is a submatrix of size 2 × 2. A quadruplet U-statistic is the average of a function on a quadruplet over all the quadruplets of a matrix. We prove several asymptotic results for quadruplet U-statistics on row-column exchangeable matrices, including a weak convergence result in the general case and a central limit theorem when the matrix is also dissociated. These results are applied to statistical inference in network analysis. We suggest a method to perform parameter estimation, network comparison and motifs count for a particular family of row-column exchangeable network models: the bipartite expected degree distribution (BEDD) models. These applications are illustrated by simulations.