  A C*-algebra $\mathfrak E$ associated with a dynamical system on a metric
graph is introduced. The system is governed by the wave equation and controlled
from boundary vertices. Algebra $\mathfrak E$ is generated by the so-called
{\it eikonals}, which are self-adjoint operators related with reachable sets of
the system. Its structure is the main subject of the paper. We show that
$\mathfrak E$ is a direct sum of "elementary blocks". Each block is an algebra
of operators multiplying ${\mathbb R}^n$-valued functions by continuous
matrix-valued functions of special kind. The eikonal algebra is determined by
the boundary inverse data. This shows promise of its possible applications to
inverse problems.
