Probabilistic graphical models, such as Bayesian networks, allow representing conditional

independence information of randomvariables. These relations are graphically represented

by the presence and absence of arcs and edges between vertices. Probabilistic graphical

models are nonunique representations of the independence information of a joint proba-

bility distribution. However, the concept of Markov equivalence of probabilistic graphical

models is able to oer unique representations, called essential graphs. In this survey paper

the theory underlying these concepts is reviewed.

Probabilistic graphical models, such as Bayesian networks, allow representing conditional independence information of randomvariables. These relations are graphically represented by the presence and absence of arcs and edges between vertices. Probabilistic graphical models are nonunique representations of the independence information of a joint probability distribution. However, the concept of Markov equivalence of probabilistic graphical models is able to oer unique representations, called essential graphs. In this survey paper the theory underlying these concepts is reviewed.