Combinatorial Data

This page contains some collections of combinatorial data.

Other useful resources include:

We have a list of graph generators.

Graph formats

Unless otherwise specified, graphs are presented in either graph6 or sparse6 format. The extension on the file name (.g6 or .s6) indicates which is used in each case. See here for information on how to use these formats. Large files are gzipped and have an additional .gz extension.


Except where it is indicated that the data was compiled by someone else, Brendan McKay releases all the data files (but not the html files) in this collection under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.

Various simple graphs

The graphs page has some collections of general graphs, eulerian graphs, chordal graphs, strongly regular graphs, Ramsey graphs, hypohamiltonian graphs, planar graphs, self-complementary graphs, highly irregular graphs, circulant graphs and extremal graphs.

Directed graphs

Some tournaments, self-complementary tournaments, locally-transitive tournaments, Ramsey tournaments, vertex-transitive tournaments, acyclic directed graphs, and posets are available on the digraphs page.

Various plane graphs

The plane graphs page has some graphs imbedded in the plane that are hard to make using plantri.


The trees page has some small trees classified by order and diameter.

Greechie diagrams

Greechie diagrams are a particular sort of hypergraph used in quantum physics to represent orthomodular lattices. They have their own page.

Latin squares and cubes

The Latin squares page has the Latin squares of small order.

The Latin cubes page has the Latin cubes and hypercubes of small order.

Hadamard matrices

The Hadamard matrix page has the Hadamard matrices up to order 32.


Some counts of regular multigraphs appear on the integer matrix page.

Maximum dissociated sets of 0-1 vectors

The dissociated sets page contains some of these things that occur in weighing problems.


Page Master: Brendan McKay, and