  We construct a bosonic quantum field on a general quantum graph. Consistency
of the construction leads to the calculation of the total scattering matrix of
the graph. This matrix is equivalent to the one already proposed using
generalized star product approach. We give several examples and show how they
generalize some of the scattering matrices computed in the mathematical or
condensed matter physics litterature.
  Then, we apply the construction for the calculation of the conductance of
graphs, within a small distance approximation. The consistency of the
approximation is proved by direct comparison with the exact calculation for the
`tadpole' graph.
