  The representation of the resolvent as an integral operator, the $m$
function, and the associated spectral representation are fundamental topics in
the spectral theory of self-adjoint ordinary differential operators. Versions
of these are developed here for canonical systems $Ju'=-zHu$ of arbitrary
order. A classical result shows that canonical systems of order two can be used
to realize arbitrary spectral data, in the form of $m$ functions from the upper
half plane to itself. In this paper, canonical systems on graphs, not
necessarily compact but with finitely many vertices, are introduced and proved
to be unitarily equivalent to certain higher order canonical systems. It is
shown that any Schr\"odinger operator on a graph is unitarily equivalent to a
canonical system on the same graph. Consequently, for an arbitrary canonical
system or Schr\"odinger operator on a graph, a representation of the resolvent
as an integral operator and a spectral representation are obtained.
