  Laplace operators on metric graphs give rise to Klein-Gordon and wave
operators. Solutions of the Klein-Gordon equation and the wave equation are
studied and finite propagation speed is established. Massive, free quantum
fields are then constructed, whose commutator function is just the Klein-Gordon
kernel. As a consequence of finite propagation speed Einstein causality (local
commutativity) holds. Comparison is made with an alternative construction of
free fields involving RT-algebras.
