@article{Banasiak2022, 
author = {Jacek Banasiak and Adam Błoch},
title = {Telegraph systems on networks and port-Hamiltonians. Ⅱ. Network realizability},
year = {2022},
journal = {Networks and Heterogeneous Media},
volume = {17},
number = {1},
pages = {73-99},
keywords = {Hyperbolic systems on networks, 1-D hyperbolic systems, graph realizability, line graphs, adjacency matrix},
url = {https://www.sciopen.com/article/10.3934/nhm.2021024},
doi = {10.3934/nhm.2021024},
abstract = {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  ×  2 hyperbolic equations on a metric graph    Γ. This is achieved by interpreting the matrix of the boundary conditions as a potential map of vertex connections of    Γ and then showing that, under the derived assumptions, that matrix can be used to determine the adjacency matrix of    Γ.}
}