A tree decomposition is a mapping of a graph into a related tree with desirable properties that allow it to be used to efficiently compute certain properties (e.g., independence
polynomial) of the original graph. The tree decomposition of a graph is not unique
and need not be isomorphic to the original graph. Tree decompositions are also known
as clique trees, join trees, and junction trees.

A measure of the count of original graph vertices mapped onto any tree vertex in
an optimal tree decomposition is known as the treewidth.