River Networks

In this chapter we review a particular case of graphs composed by river networks. These geophysical graphs are a particular kind of network. Given its physical properties, they do not have “loops” (technically “cycles”) and are therefore better designed by the term “trees”. Knowledge of these structures is nowadays extremely important especially for the increasing value that freshwater resources are assuming in our society. As graphs they are particularly important as a paradigmatic example of transportation graphs and for the possibility to define energy functionals to describe their evolution.