Moral graph

A moral graph is a concept in graph theory, used to find the equivalent undirected form of a directed acyclic graph. It is a key step of the junction tree algorithm, used in belief propagation on graphical models.

The moralized counterpart of a directed acyclic graph is formed by connecting nodes that have a common child, and then making all edges in the graph undirected. The name stems from the fact the two nodes that have a common child are said to be married. Equivalently, a moral graph of a directed acyclic graph G is an undirected graph in which each node of the original G is now connected to its Markov blanket.

A directed acyclic graph.

The corresponding moral graph. The newly added arcs are shown in red in the moralized graph.

See also

• D-separation
• Tree decomposition

References

• Cowell, Robert G.; Dawid, A. Philip; Lauritzen, Steffen L., Spiegelhalter, David J. (1999). "3.2.1 Moralization". Probabilistic Networks and Expert Systems. Springer-Verlag New York. pp. 31–33. ISBN 0-387-98767-3. 
• M. Studeny: On mathematical description of probabilistic conditional independence structures