Laplace–Beltrami operators on decorated graphs

We discuss Laplace–Beltrami operators on decorated graphs, i.e., topological spaces obtained by identifying endpoints of edges of a graph with some points on closed orientable Riemannian manifolds of dimensions 1, 2, or 3. Such operators can be constructed by using the Laplace–Beltrami operators on each component with some boundary conditions at the points of gluing. And all these operators are described by lagrangian planes in some euclidean space.