Does the Wolfram database of graphs include all connected graphs when the number of vertices is <= 8?


1 Answer 1


We can get the number of connected graphs on $k$ nodes that are contained in GraphData as follows:

Table[Length@GraphData["Connected", k], {k, 1, 8}]
(* {1, 1, 2, 6, 21, 112, 853, 215} *)

Let us compare this to the total number of connected unlabelled graphs on $k$ nodes, which is recorded in OEIS A001349:

1, 1, 2, 6, 21, 112, 853, 11117

We see that up to 7 nodes, GraphData has all of them. But it only has 215 connected graphs on 8 nodes, while the total number is 11,117.


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