A class of graphs is introduced which is closed under marginalizing and conditioning. It is shown that these operations can be executed by performing in arbitrary order a sequence of simple, strictly local operations on the graph at hand. The results are based on a simplification of J. Pearl's notion of $d$-separation. As the simplification does not change the separation properties of graphs for which the original $d$-separation concept is applicable (e.g., directed graphs), it constitutes a true generalization of the latter concept to the present class of graphs.
"Marginalizing and conditioning in graphical models." Bernoulli 8 (6) 817 - 840, December 2002.