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.

- Edge deletion
- Start with a full graph
- Check each edge and see if removing it violates the I-mapness of the graph
- Determine whether fixing the values of all other variables in the graph renders these two independent

- Markov boundary
- For each variable, add edges until it has a sufficient Markov boundary

- [http://en.wikipedia.org/wiki/Moral_graph Moralization]

- Starting with a Bayesian Network
- Connect the parents of all convergent nodes

- Fill-In Method
- Starting with a Bayesian Network
- Use the fill-in method to create a Tree Decomposition

Deviant case:

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.