  Hyperbolic systems on networks often can be written as systems of first order
equations on an interval, coupled by transmission conditions at the endpoints,
also called port-Hamiltonians. However, general results for the latter have
been difficult to interpret in the network language. The aim of this paper is
to derive conditions under which a port-Hamiltonian with general linear
Kirchhoff's boundary conditions can be written as a system of $2\times 2$
hyperbolic equations on a metric graph $\Gamma$. This is achieved by
interpreting the matrix of the boundary conditions as a potential map of vertex
connections of $\Gamma$ and then showing that, under the derived assumptions,
that matrix can be used to determine the adjacency matrix of $\Gamma$.
