Moral graph

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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. 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. The name stems from the fact that, in a moral graph, two nodes that have a common child are required to be married by sharing an edge.

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

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