Tree decomposition
（重定向自Clique tree）
![A graph with eight vertices, and a tree decomposition of it onto a tree with six nodes. Each graph edge connects two vertices that are listed together at some tree node, and each graph vertex is listed at the nodes of a contiguous subtree of the tree. Each tree node lists at most three vertices, so the width of this decomposition is two.](/Images/godic/202501/05/Tree_decomposition.svg1552.png")
![Two different tree-decompositions of the same graph](/Images/godic/202501/05/Treedecompsnocolour1552.JPG")
In graph theory, a tree decomposition is a mapping of a graph into a tree that can be used to define the treewidth of the graph and speed up solving certain computational problems on the graph.
In machine learning, tree decompositions are also called junction trees, clique trees, or join trees; they play an important role in problems like probabilistic inference, constraint satisfaction, query optimization, and matrix decomposition.