  Network flows and specifically open canal flows can be modeled by systems of
balance laws defined on topological graphs. The shallow water or Saint-Venant
system of balance laws is one of the most used model and present two phases:
fluvial or sub-critical and torrential or super critical. Phase transitions may
occur within the same canal but transitions related to networks are less
investigated. In this paper we provide a complete characterization of possible
phase transitions for a simple network with two canals and one junction. Our
analysis allows the study of more complicate scenarios. Moreover, we provide
some numerical simulations to show the theory at work.
