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The algebra of eikonals $\mathfrak E$ of a metric graph $\Omega$ is anoperator $C^*$-algebra determined by dynamical system with boundary controlthat describes wave propagation on the graph. In this paper, two canonicalblock forms (algebraic and geometric) of the algebra $\mathfrak E$ are providedfor an arbitrary connected locally compact graph. These forms determine somemetric 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 ordinarygraphs is introduced, whose frames are identical: $\mathfrak F^{\,\rma}\equiv\mathfrak F^{\,\rm g}$. The results are supposed to be used in theinverse problem that consists in determination of the graph from its boundaryinverse data.

Canonical forms of metric graph eikonal algebra and graph geometry