Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient estimation of a Gromov--Hausdorff distance between unweighted
  graphs   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 \cite{memoli12}
(M\'emoli, F, \textit{Discrete \& Computational Geometry, 48}(2) 416-440,
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.

9
The categories of this paper are: nlin
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph