The city is built on islands, some of which are connected by bridges. There is a maximum of one bridge between two islands, you can only go one way over the bridge, but you can get from any island to any other by no more than two bridges. One bridge was closed for repairs, but you can still get to each from each island. Prove that for any pair of islands it is possible to get from one to another by at most three bridges.
I have drawn a directed graph with 5 vertices and 10 edges which satisfies the initial conditions. However I have no idea what to do next, removing any edge does indeed lead to any other island being reachable in 3 or less bridges, but how to I go about proving it for any v vertices and any e edges? And proving it for my specific example with 5 vertices too in fact.