graphscope.nx.generators.atlas.graph_atlas_g

graphscope.nx.generators.atlas.graph_atlas_g()[source]

Returns the list of all graphs with up to seven nodes named in the Graph Atlas.

The graphs are listed in increasing order by

  1. number of nodes,

  2. number of edges,

  3. degree sequence (for example 111223 < 112222),

  4. number of automorphisms,

in that order, with three exceptions as described in the Notes section below. This causes the list to correspond with the index of the graphs in the Graph Atlas [atlas], with the first graph, G[0], being the null graph.

Returns:

A list of Graph objects, the one at index i corresponding to the graph i in the Graph Atlas.

Return type:

list

See also

graph_atlas

Notes

This function may be expensive in both time and space, since it reads a large file sequentially in order to populate the list.

Although the NetworkX atlas functions match the order of graphs given in the “Atlas of Graphs” book, there are (at least) three errors in the ordering described in the book. The following three pairs of nodes violate the lexicographically nondecreasing sorted degree sequence rule:

  • graphs 55 and 56 with degree sequences 001111 and 000112,

  • graphs 1007 and 1008 with degree sequences 3333444 and 3333336,

  • graphs 1012 and 1213 with degree sequences 1244555 and 1244456.

References

[atlas]

Ronald C. Read and Robin J. Wilson, An Atlas of Graphs. Oxford University Press, 1998.