  We consider arbitrary quantum wire networks modelled by finite, noncompact,
connected quantum graphs in the presence of an external magnetic field.
  We find a general formula for the total scattering matrix of the network in
terms of its local scattering properties and its metric structure. This is
applied to a quantum ring with $N$ external edges. Connecting the external
edges of the ring to heat reservoirs, we study the quantum transport on the
graph in ambient magnetic field. We consider two types of dynamics on the ring:
the free Schr\"odinger and the free massless Dirac equations. For each case, a
detailed study of the thermal noise is performed analytically.
  Interestingly enough, in presence of a magnetic field, the standard linear
Johnson-Nyquist law for the low temperature behaviour of the thermal noise
becomes nonlinear. The precise regime of validity of this effect is discussed
and a typical signature of the underlying dynamics is observed.
