Getting and analyzing biological interaction networks is at the core of systems biology. To
help understanding these complex networks, many recent works have suggested to focus on …

Publisher Summary Networks are ubiquitous. They arise naturally as models of
communication networks, networks of friends, in the communication of infection, rumors or …

W-graph refers to a general class of random graph models that can be seen as a random
graph limit. It is characterized by both its graphon function and its motif frequencies. In this …

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 …

We consider $ U $-statistics on row-column exchangeable matrices. We derive a
decomposition for them, based on orthogonal projections on probability spaces generated …

Various methods have been recently employed to characterise the structure of biological
networks. In particular, the concept of network motif and the related one of coloured motif …

The work presented in this thesis is essentially theoretical, but motivated by ecological
applications. Ecological interaction networks represent the functioning of an ecosystem …

Small subgraph counts can be used as summary statistics for large random graphs. We use
the Stein–Chen method to derive Poisson approximations for the distribution of the number …

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 …

W-graph refers to a general class of random graph models that can be seen as a random
graph limit. It is characterized by both its graphon function and its motif frequencies. The …