  Gromov-Hausdorff distances measure shape difference between the objects
representable as compact metric spaces, e.g. point clouds, manifolds, or
graphs. Computing any Gromov-Hausdorff distance is equivalent to solving an
NP-Hard optimization problem, deeming the notion impractical for applications.
In this paper we propose polynomial algorithm for estimating the so-called
modified Gromov-Hausdorff (mGH) distance, whose topological equivalence with
the standard Gromov-Hausdorff (GH) distance was established in M\'emoli F,
2012. We implement the algorithm for the case of compact metric spaces induced
by unweighted graphs as part of Python library $\verb|scikit-tda|$, and
demonstrate its performance on real-world and synthetic networks. The algorithm
finds the mGH distances exactly on most graphs with the scale-free property. We
use the computed mGH distances to successfully detect outliers in real-world
social and computer networks.
