  We extend the general stochastic matching model on graphs introduced in
(Mairesse and Moyal, 2016), to matching models on multigraphs, that is, graphs
with self-loops.
  The evolution of the model can be described by a discrete time Markov chain
whose positive recurrence is investigated.
  Necessary and sufficient stability conditions are provided, together with the
explicit form of the stationary probability in the case where the matching
policy is `First Come, First Matched'.
