  The study of the scattering data for a star-shape network of LC-transmission
lines is transformed into the scattering analysis of a Schr\"odinger operator
on the same graph. The boundary conditions coming from the Kirchhoff rules
ensure the existence of a unique self-adjoint extension of the mentioned
Schr\"odinger operator. While the graph consists of a number of infinite
branches and a number finite ones, all joining at a central node, we provide a
construction of the scattering solutions. Under non-degenerate circumstances
(different wave travelling times for finite branches), we show that the study
of the reflection coefficient in the high-frequency regime must provide us with
the number of the infinite branches as well as the the wave travelling times
for finite ones.
