  Nonlinear quantum graphs are metric graphs equipped with a nonlinear
Schr{\"o}dinger equation. Whereas in the last ten years they have known
considerable developments on the theoretical side, their study from the
numerical point of view remains in its early stages. The goal of this paper is
to present the Grafidi library, a Python library which has been developed with
the numerical simulation of nonlinear Schr{\"o}dinger equations on graphs in
mind. We will show how, with the help of the Grafidi library, one can implement
the popular normalized gradient flow and nonlinear conjugate gradient flow
methods to compute ground states of a nonlinear quantum graph. We will also
simulate the dynamics of the nonlinear Schr{\"o}dinger equation with a
Crank-Nicolson relaxation scheme and a Strang splitting scheme. Finally, in a
series of numerical experiments on various types of graphs, we will compare the
outcome of our numerical calculations for ground states with the existing
theoretical results, thereby illustrating the versatility and efficiency of our
implementations in the framework of the Grafidi library.
