Encyclopedia of Finite Graphs
Integer sequence discovery from small graphs, also published in the August 2015 journal of Discrete Applied Mathematics.
This project has three major aims,
- To build an exhaustive reference database for graph invariants of a given class.
- To "mine" this database for sequences not present (or incomplete) in the OEIS.
- To use these sequences to suggest new mathematical relations between graph invariants.
The Encyclopedia calls upon many external libraries to generate the data.
To fully repopulate the database, it requires
As an alternative, there is a standalone version of of the simple connected graph database for download.
Integer Sequences Discovered
A catalog of all the sequences discovered and submitted to the OEIS.
Sequence Extensions: Sequences present in the OEIS, but extended.
Distinct Sequences: Sequences generated by distinct classes.
New Primary Sequences: Sequences generated by a single invariant conditions.
Secondary Sequences: Sequences generated by paired invariant conditions.
Once the database is built, invariant conditions can be explored. For example, to display the only the three graphs that are simultaneously bipartite, integral and Eulerian with ten vertices:
python viewer.py 10 -i is_bipartite 1 -i is_integral 1 -i is_eulerian 1
First compile the invariant calculations, and run the unit test on the Petersen graph:
make compile make test
You can automatically download an updated copy of the database by cloning the database repository in the Encyclopedia directory:
git submodule add https://github.com/thoppe/Simple-connected-graph-invariant-database.git database
Note that we are unable to store the special invariants for larger graphs due to size constraints; these larger special invariants will have to be recomputed for
We recommend rebuilding portions of the database as both a consistency check and a learning tool if you are considering adding additional invariants.
If the database has been updated, you can grab a new copy by running:
git submodule foreach git pull origin master
n_cycle_basisof which the n=0 case
chromatic_polynomialleads to the
k_edge_connectivityminimal number of nodes/edges that can be deleted to disconnect the graph.
Note that older versions of the database incorrectly labeled
is_subgraph_free_K3of which the n=0 case is a triangle-free graph. (graph_tool)
is_subgraph_free_C10checks for cycles of length k (graph_tool)
maximal_independent_vertex_setalso called the Independence number,
n_independent_edge_setsalso called the Hosoya Index.
Other Invariants (hard)
Other Invariants (trivial)