An example of a case where the person will reach his home almost surely is when the lengths of all the blocks are between "a" and "b" (where "a" and "b" are any two finite positive numbers). Notice that we do not assume that the graph is planar, i.e. the city may contain tunnels and bridges. One way to prove this result is using the connection to electrical networks. Take a map of the city and place a one ohm resistor on every block. Now measure the "resistance between a point and infinity." In other words, choose some number "R" and take all the points in the electrical network with distance bigger than "R" from our point and wire them together. This is now a finite electrical network, and we may measure the resistance from our point to the wired points. Take "R" to infinity. The limit is called the "resistance between a point and infinity". It turns out that the following is true (an elementary proof can be found in the book by Doyle and Snell):