Number of Connected simple graphs with n vertices Is there a relation between numbers of simple graphs and simple connected graphs on n vertices? After observing n=1,2,3,4...., I noticed that the number of connected graphs is at least half of the total number of simple graphs. How can we prove that?

The number of nonisomorphic simple graphs is A88 and the number of connected simple graphs is A1349 in the OEIS. They are related by the Euler transform; this is a special case of the Multiset Transformation, which means the not necessarily connected graphs are multisets of the connected graphs.
