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.