 Take two graphs formula_59 and formula_127 on the same vertex set.Because these graphs share the same vertices,
one way to measure their distance is to restrict to subsets formula_166 of the vertex set, and for each such pair subsets compare the number of edges formula_167 from formula_168 to formula_169 in formula_59 to the number of edges formula_171 between formula_168 and formula_169 in formula_127.If these numbers are similar for every pair of subsets (relative to the total number of vertices), then that suggests formula_59 and formula_127 are similar graphs.