Suppose we are talking about graphs with $n$ labeled vertices. Which graphs are more common: connected or disconnected?



Are there more connected or disconnected graphs on $n$ vertices?
Connectedness wins, since the complement of any disconnected graph is connected.


EDIT: Perhaps you'd like a proof of this. Let G be a disconnected graph, G' its complement. If v and u are in different components of G, then certainly they're connected by an edge in G'. And if they're in the same component of G, then there's some w in another component (since G was disconnected), so v-w-u is a path in G'.


