This is actually really useful - you have a map of 'what is the fastest way home from anywhere in the city?' On moving to a new city, getting a map like this and memorising a few of the arteries would help loads with familiarization.
If you are busing... Sure the argument can be made that this doesn't take into account light-timers for walking, but if you're greedily selecting for shortest distance, this is exactly what you want when walking.
Transit heat maps are generally used for autos and buses, but could just as easily be made for walking. You'd just code the average wait time for timers into the heat map algorithm.
Yes - one of the classical ways of computing betweeness centrality is to calculate the number of shortest paths passing through each edge. In this case however, he's only computing the shortest paths to/from a single vertex.
Very interesting. How are the roads weighted in this? Meaning is there any travel time involved? Or is it just length? It would be interesting to play with different weighting and see if it changes.
Nitpick: I don't think the world flights to Paris map is correct. It shows flights from Noumea, New Caledonia going through Australia. The shorter route is through Seoul.
