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) In the unlikely event that I am the first to think about using that operation, which symbols should I NOT use to denote it in order to avoid confusion with other graph products?
UPDATE: I have now asked this question on MathOverflow as well.