Counting connected graphs asymptotically

We find the asymptotic number of connected graphs with k vertices and k − 1 + l edges when k , 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 ) for an appropriate edge probability p . Central is the analysis of a random walk with fixed beginning and end which is tilted to the left.