In topology, a graph manifold (in German: Graphenmannigfaltigkeit) is a 3-manifold which is obtained by gluing some circle bundles.
They were discovered and classified by the German topologist Friedhelm Waldhausen in 1967.
Two very important classes of examples are given by the Seifert bundles and the Solv manifolds.
From this perspective, Waldhausen's article can be seen as the first breakthrough towards the discovery of JSJ decomposition.
One of the numerous consequences of the Thurston-Perelman geometrization theorem is that graph manifolds are precisely the 3-manifolds whose Gromov norm vanishes.