  We consider a stochastic matching model with a general compatibility graph,
as introduced in \cite{MaiMoy16}. We show that the natural necessary condition
of stability of the system is also sufficient for the natural matching policy
'First Come, First Matched' (FCFM). For doing so, we derive the stationary
distribution under a remarkable product form, by using an original dynamic
reversibility property related to that of \cite{ABMW17} for the bipartite
matching model.
