Suppose that we have a standard TSP, except that it is required to visit each city at least once instead of exactly once. The challenge is: how to transform this problem to a standard TSP? To that end, one construct a new network with arcs representing the shortest paths between each pair of nodes.
Now the TSP with multiple city visits is equivalent to a standard TSP defined on the new network.
Q: Can somebody explain why TSP with multiple city visits on the original network is equivalent to a standard TSP defined on the new network?