The algebra of eikonals $\mathfrak E$ of a metric graph $\Omega$ is an
operator $C^*$-algebra determined by dynamical system with boundary control
that describes wave propagation on the graph. In this paper, two canonical
block forms (algebraic and geometric) of the algebra $\mathfrak E$ are provided
for an arbitrary connected locally compact graph. These forms determine some
metric graphs (frames) $\mathfrak F^{\,\rm a}$ and $\mathfrak F^{\,\rm g}$.
Frame $\mathfrak F^{\,\rm a}$ is determined by the boundary inverse data. Frame
$\mathfrak F^{\,\rm g}$ is related to graph geometry. A class of ordinary
graphs is introduced, whose frames are identical: $\mathfrak F^{\,\rm
a}\equiv\mathfrak F^{\,\rm g}$. The results are supposed to be used in the
inverse problem that consists in determination of the graph from its boundary
inverse data.

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