A Markov Network a.k.a. Markov Random Field is an undirected Dependency Graph which is a minimal I-map of a probability distribution. As a minimal I-map, deleting any edge destroys its Markov property.
Unlike a Bayesian network, a Markov network is undirected and may contain cycles.
The Markov blanket of a variable is the set of other variables which can be conditioned upon to achieve independence with the rest of the graph. The Markov boundary is a minimal Markov blanket.
Also see WP:Markov random field
Can be constructed for any positive probability distribution which satisfies dependency graph properties.
Deviant case: $x=y=z=t$ A minimal I-map for this case is any tree because each variable is independent of the rest only conditioned on a third. This is difficult to find with the previous construction methods because it isn't a well-behaved probability distribution.