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) \(\mathfrak F^{\,\mathrm a}\) and \(\mathfrak F^{\,\mathrm g}\) . Frame \(\mathfrak F^{\,\mathrm a}\) is determined by the boundary inverse data. Frame \(\mathfrak F^{\,\mathrm g}\) is related to graph geometry. A class of ordinary graphs is introduced, whose frames are identical: \(\mathfrak F^{\,\mathrm a}\equiv \mathfrak F^{\,\mathrm g}\) . The results are assumed to be used in the inverse problem that consists in determination of the graph from its boundary inverse data. Bibliography: 13 titles.
