  Routing optimization is a relevant problem in many contexts. Solving directly
this type of optimization problem is often computationally unfeasible. Recent
studies suggest that one can instead turn this problem into one of solving a
dynamical system of equations, which can instead be solved efficiently using
numerical methods. This results in enabling the acquisition of optimal network
topologies from a variety of routing problems. However, the actual extraction
of the solution in terms of a final network topology relies on numerical
details which can prevent an accurate investigation of their topological
properties. In this context, theoretical results are fully accessible only to
an expert audience and ready-to-use implementations for non-experts are rarely
available or insufficiently documented. In particular, in this framework, final
graph acquisition is a challenging problem in-and-of-itself. Here we introduce
a method to extract networks topologies from dynamical equations related to
routing optimization under various parameters' settings. Our method is made of
three steps: first, it extracts an optimal trajectory by solving a dynamical
system, then it pre-extracts a network and finally, it filters out potential
redundancies. Remarkably, we propose a principled model to address the
filtering in the last step, and give a quantitative interpretation in terms of
a transport-related cost function. This principled filtering can be applied to
more general problems such as network extraction from images, thus going beyond
the scenarios envisioned in the first step. Overall, this novel algorithm
allows practitioners to easily extract optimal network topologies by combining
basic tools from numerical methods, optimization and network theory. Thus, we
provide an alternative to manual graph extraction which allows a grounded
extraction from a large variety of optimal topologies.
