  In many real-world applications data come as discrete metric spaces sampled
around 1-dimensional filamentary structures that can be seen as metric graphs.
In this paper we address the metric reconstruction problem of such filamentary
structures from data sampled around them. We prove that they can be
approximated, with respect to the Gromov-Hausdorff distance by well-chosen Reeb
graphs (and some of their variants) and we provide an efficient and easy to
implement algorithm to compute such approximations in almost linear time. We
illustrate the performances of our algorithm on a few synthetic and real data
sets.
