I asked this a week ago on math.SE, but haven't obtained an answer yet, so I hope it is fine to ask this here too.

Let $G$ and $H$ be two possibly directed, non necessarily simple, vertex-labelled graphs with respective adjacency matrices $A_G$ and $A_H$ and $V(G)=V(H)$.

1) What is the name of the graph $M$ with adjacency matrix $A_M=A_HA_G$?

2) Which symbols should I NOT use to denote it in order to avoid confusion with other graph products, in the event that none is already associated with this operation?