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This is using nauty's internal dense format, described in nauty and Traces User’s Guide (Version 2.8.6) section 3.
Here's a hacky way to get a graph out of it:
set_length = len(g1) // g.number_of_vertices
sets = [g1[set_length*k:set_length*(k+1)] for k in range(g.number_of_vertices)]
neighbors = [[i for i in range(set_length * 8) if st[-1 - i//8] & (1 << (7 - i%8))] for st in sets]
g_canon = Graph(number_of_vertices=g.number_of_vertices, directed=False, adjacency_dict={i: neighbors[i] for i in range(g.number_of_vertices)})
Check:
>>> certificate(g_canon) == certificate(g)
True
>>> from pynauty import canon_label
>>> canon_label(g_canon)
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18]
(Cross-posted from https://github.com/pdobsan/pynauty/issues/30#issuecomment-1564066767.)
