Mike van Santvoort | Searcharxiv

arXiv2026

Flexible random graph modeling for cell-cell interactions

In this paper we explore generalisations to a random digraph model designed for modelling cell-cell interactions (RaCInG). In its baseline model -- tested both theoretically and in biological practice -- a fixed number of arcs are assigned uniformly at random to vertices that have suitable types to accept them. Generalisations to this model are explored in two directions: creating undirected graphs in favour of directed graphs, and incorporating spatial information. Both directions are driven by biological demands: better interpretability and adaptation to technological advances. We show not only that these generalisations are theoretically possible within the framework of RaCInG, but that they can be made rigorous, proving that RaCInG creates a flexible random graph framework to model cell-cell interactions.

math.PR↗

arXiv2023

From inhomogeneous random digraphs to random graphs with fixed arc counts

Consider a random graph model with $n$ vertices where each vertex has a vertex-type drawn from some discrete distribution. Suppose that the number of arcs to be placed between each pair of vertex-types is known, and that each arc is placed uniformly at random without replacement between one of the vertex-pairs with matching types. In this paper, we will show that under certain conditions this random graph model is equivalent to the well-studied inhomogeneous random digraph model. We will use this equivalence in three applications. First, we will apply the equivalence on some well known random graph models (the Erdős-Rényi model, the stochastic block model, and the Chung-Lu model) to showcase what their equivalent counterparts with fixed arcs look like. Secondly, we will extend this equivalence to a practical model for inferring cell-cell interactions to showcase how theoretical knowledge about inhomogeneous random digraphs can be transferred to a modeling context. Thirdly, we will show how our model induces a natural fast algorithm to generate inhomogeneous random digraphs.

math.PR↗