Interacting particle systems where particles interact via coagulation are of great interest for their various behaviours. In particular, interesting phenomena can occur, depending on the structure of the kernel which is giving a rate to each coagulation. Among these phenomena there is the famous phase transition that goes under the name of gelation, i.e. the appearence of one (or multiple) giant particle(s). Although fluid limits are known for the rescaled version of stochastic coagulation processes (convergence to the Smoluchowski coagulation equation and its modification), very few is known about large deviations and rare events in this framework. In this talk we will explore some connections of these processes with random graphs and how to use this connection to attack the problem of studying large deviations. This also allows a comparison with the phase transition in graphs, where a giant component appears. Some remarks about the possible generalization to coagulation kernels that depend on spatial position will be given. This is based on ongoing joint works with Wolfgang K ̈onig (WIAS and TU Berlin), Tejas Iyer (WIAS), Heide Langhammer (WIAS), Elena Magnanini (WIAS) and Robert Patterson (WIAS).