pub fn expected_walk_length_on_football()Expand description
Run this to get the answer to the first part of the question.
Interestingly, switching to calculate_with_limit and running this with a walk-length limit even as high as 80 or 90 seems to give the wrong picture. The expected value appears to vary significantly even as we continue increasing the walk length limit to high values, so very long walks are contributing to the result (it is a fat-tailed distribution). This is corroborated when we print out the frequency map and see that we are getting plenty of walks which are several hundred steps long.
Using the calculate method which imposes no limitation on walk-lengths, but takes longer to run, we seem to immediately be converging on an expected walk-length of 20 (which is of course the total number of nodes in the graph). This is an interesting result, and one we later proved rigorously (see crate-level documentation).