Thursday, September 15, 2022

[DMANET] House of Graphs 2.0: a database of interesting graphs and more

In 2012 we announced the website "the House of Graphs"
( through this mailing list.

The House of Graphs hosts complete lists of graphs of various graph
classes (such as cographs, cubic graphs, fullerenes, hypohamiltonian
graphs, snarks, trees,...). But its main feature is a searchable
database of so called "interesting" graphs. That includes graphs that
already occurred as counterexamples to conjectures or as extremal graphs
or in other contexts.

The key idea is that although already for small orders extremely many
graphs exist, there are some that serve again and again as
counterexamples and that a database of these graphs should be
established. In this database one can e.g. search for graphs with
certain invariant values, graphs with a certain name (e.g. Petersen,
Heawood, Coxeter, etc.) or graphs that are marked as being "interesting"
for a certain invariant (e.g. marked as being interesting for the
chromatic number). These searches can of course also be combined and the
results can be downloaded so that one gets good candidates for testing
new conjectures one is working on.

An important feature is that users can add graphs to the database. If
the graphs are not yet in the database, the system computes invariant
values for the graphs. So the database can also be used as a repository.
If you discover new interesting graphs, you can make them available to
users by submitting them to the database together with a text identifier
(e.g. counterexample_this_conjecture) or by referring to their HoG graph
id. Then other scientists can find and download the graph from the House
of Graphs.

Over the years, several new features and invariants were added to the
House of Graphs and users uploaded many interesting graphs to the
website. But as the development of the original House of Graphs website
started in 2010, the underlying frameworks and technologies of the
website became outdated. This is why in 2021-2022, the House of Graphs
was rebuilt completely, using modern frameworks to build a maintainable
and expandable web application that is future-proof. On top of this, new
functionalities were added to improve the application and the user
experience. A selection of new features includes:

- Several new graph invariants were added (such as: automorphism group
size, number of vertex orbits, treewidth, traceability,
hypohamiltonicity,....) and several existing invariant computers were
replaced by faster implementations.
- A new graph drawing tool which can also import graphs from a file to
generate an automated drawing which can then be altered manually.
- It is now possible to add multiple drawings per graph.
- It is now also possible to edit the drawings of a given graph.
- Graph drawings can be exported to various formats (svg, png, pdf,
- The new website renders much more nicely on mobile devices.

The entire database of the old House of Graphs was migrated to the new
website, so all graphs (and their associated HoG graph id), comments,
accounts, etc. are preserved.

The new website also comes with a new url: but
the old url also points to the new website and
will remain active in the near future for backwards compatibility.

More information on "the House of Graphs" (including a video tutorial)
can be found on

and in:

House of Graphs: a database of interesting graphs, Discrete Applied
Mathematics, 161(1-2):311-314, 2013.
Available online:
Or on arXiv:

We hope that you will enjoy the new website.

Gunnar Brinkmann, Kris Coolsaet, Sven D'hondt, Jan Goedgebeur and
Hadrien Mélot

Jan Goedgebeur
Department of Computer Science
KU Leuven Campus Kulak
Etienne Sabbelaan 53
8500 Kortrijk, Belgium

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