An I-map (independence map) for a Probability distribution $P$ is any Graphical model $G$ such that the set of independences implied by the network ($I(G)$) is a subset of the set of independences of $P$ ($I(P)$) (see here), i.e. $I(G) \subset I(P)$

A perfect (independence) map is one such that $I(G) = I(P)$

I-maps and perfect maps.

Independence of random variables – vid

Independence and factors