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.
[*] At present, Traces does not accept digraphs.
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 2.7 (r1) of nauty, and version 2.1 of Traces, as a gzipped tar file (∼3.4 MB).
See the file changes24-27.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.
Installation proceduretar xvzf nauty27r1.tar.gz
After this procedure, the directory nauty27r1 contains all the executables. Move them somewhere else as you wish.
Type An to enter nauty dense mode, As for nauty sparse mode, At for Traces mode. Type an additional + to convert the current graph. With a few exceptions, all dreadnaut 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 nauty mailing list so that you can receive notices of updates and exchange information with other users.
News and comments
This edition of the source code and installation scripts has been tested on a variety of Unix/Linux systems (including MacOS X), but many systems remain untested. Please send your success and failure stories. Note that old or broken systems may not be supported at all; try an older version of nauty. A few utilities such as shortg require a Unix-like environment.
dretodot is a tool for drawing graphs in dreadnaut format; it produces a .dot file which can be rendered by Graphviz. Click below for a short video tutorial.
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.
Licensed 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 https://www.apache.org/licenses/LICENSE-2.0.
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)