Finite propagation speed for solutions of the wave equation on metric   graphs
  We provide a class of self-adjoint Laplace operators on metric graphs with the property that the solutions of the associated wave equation satisfy the finite propagation speed property. The proof uses energy methods, which are adaptions of corresponding methods for smooth manifolds. 
Vadim Kostrykin, J\"urgen Potthoff, Robert Schrader
math-ph math.MP