  The eikonal algebra $\mathfrak E$ of the metric graph $\Omega$ is an operator
$C^*$--algebra defined by the dynamical system which describes the propagation
of waves generated by sources supported in the boundary vertices of $\Omega$.
This paper describes the canonical block form of the algebra $\mathfrak E$ of
an arbitrary compact connected metric graph. Passing to this form is equivalent
to constructing a functional model which realizes $\mathfrak E$ as an algebra
of continuous matrix-valued functions on its spectrum $\widehat{\mathfrak{E}}$.
The results are intended to be used in the inverse problem of reconstruction of
the graph by spectral and dynamical boundary data.
  Bibliography: 28 items.
