Stochastic SIR-type epidemic processes on random graphs are a special class of interaction networks that have become of interest lately for modeling contact-type epidemics (Ebola, HIV, election choices etc). I will discuss a particular case of the SIR epidemic evolving on a configuration model random graph with given degree distribution. In particular, I will describe the relevant large graph limit result which yields the law of large numbers (LLN) for the edge-based SIR process and is useful in building a "network-free" SIR Markov hybrid model for epidemic parameters inference.