Counting connected graphs asymptotically

We find the asymptotic number of connected graphs with kk vertices and k−1+lk−1+l edges when k,lk,l approach infinity, re-proving a result of Bender, Canfield and McKay. We use the probabilistic method  , analyzing breadth-first search on the random graph G(k,p)G(k,p) for an appropriate edge probability pp. Central is the analysis of a random walk with fixed beginning and end which is tilted to the left.