# Completeness of wolfram database of graphs

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

• – user64494 Feb 18 '17 at 10:19
• @user64494 That table is for labelled graph, but GraphData does not have isomorphic duplicates. – Szabolcs Feb 18 '17 at 10:21

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}]

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.