nauty and Traces are programs for computing automorphism groups of graphs and digraphs [*].
They can also produce a canonical label. They are written in a portable subset of C, and run on a considerable number of different systems.
There is a small suite of programs called gtools included
in the package. For example, geng can generate
non-isomorphic graphs very quickly. There are also generators for
bipartite graphs, digraphs, and multigraphs, and programs for manipulating
files of graphs in a compact format.
A complete manual is included in the package. It is also
separately available here.
The original design of nauty is in McKay, B.D.,
Practical Graph Isomorphism, Congressus Numerantium, 30 (1981) 45-87.
A scan (2.6 MB) is available.
The original design of Traces is in in Piperno, A.,
Search Space Contraction in Canonical Labeling of Graphs,
available at arxiv.org.
The current algorithms behind nauty and Traces
are described in the paper of McKay and Piperno cited below.
How to cite nauty or Traces
If you use nauty or Traces in your research,
please cite this paper:
McKay, B.D. and Piperno, A.,
Practical Graph Isomorphism, II,
Journal of Symbolic Computation, 60 (2014),
pp. 94-112, https://doi.org/10.1016/j.jsc.2013.09.003
(a BibTex entry is here).
How to get it
If you agree to the restrictions listed below, you may fetch
version 2_8_6 of nauty, and version 2.2 of Traces, as a
gzipped tar file (∼3.4 MB).
See the file changes24-28.txt
for a summary of recent changes.
The package uses the GNU autoconf installation system.
You are advised to read the file README before compiling anything.
tar xvzf nauty2_8_6.tar.gz
After this procedure, the directory nauty2_8_6 contains all
the executables. Move them somewhere else as you wish.
to enter nauty dense mode,
for nauty sparse mode,
for Traces mode. Type an additional
to convert the current graph. With a few exceptions, all
commands are available in every mode.
See the manual for a full description of the new features.
Nauty mailing list
You are invited to join the
mailing list so that you can receive notices of updates and
exchange information with other users.
This is the license for the software package Nauty and
, package versions 2.6 and later.
Five categories of software are included in the package:
A. All files not listed as B-E below, copyright Brendan McKay (1984-)
B. Files traces.h, traces.h and dretodot.c, copyright Adolfo Piperno (2008-)
C. File watercluster2.c, copyright Gunnar Brinkmann (2009-)
D. Files planarity.h and planarity.c, copyright Magma project,
University of Sydney
E. Files nautycliquer.h and nautycliquer.c, copyright to Sampo
Niskanen and Patric Ostergard.
under the Apache License, Version 2.0 (the "License");
you may not use this software except in compliance with the License.
You may obtain a copy of the License at
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
Brendan McKay: Australian National University; Brendan.McKay@anu.edu.au
Adolfo Piperno: University of Rome "Sapienza"; firstname.lastname@example.org
Gunnar Brinkmann: University of Ghent; Gunnar.Brinkmann@UGent.be
Magma Administration: University of Sydney; email@example.com
Patric Ostergard: Aalto Univerity; firstname.lastname@example.org
Earlier (pre-2.6) versions of this package carried a different
notice: "Permission is hereby given for use and/or distribution
with the exception of sale for profit or application with nontrivial
military significance." These days most people use nauty via a
larger package such as Magma, Sage, or GAP, and often they don't
even know they are using nauty. Due to the legal nonsense that
large package distributors need to worry about, it has proved too
much trouble to maintain an idiosyncratic licence. I didn't change
my opinion about military use, but it is no longer part of the
formal notice. Brendan McKay (Jan 20, 2016)