I'm looking at $\mathcal{G}(n,p)$ (I'll call these Erdos-Renyi networks) where $n$ is, say, at most 10.

I would like to know the probability a random node is in a component of size $m$.

It's sufficient for me to know what the size distribution is of components in small Erdos-Renyi networks. Is there a straight-forward calculation for this?

The best I can think of at the moment is to try to take all connected graphs of size $m\leq n$, and then determine their probability of being a component of an Erdos-Renyi network. It's not obvious to me how to deal with this since I don't know a straightforward way to enumerate all connected graphs of size $m$ (though given such a connected graph, it's straightforward to calculate it's probability of being a component of an Erdos-Renyi network)