No More Shortest Path

You are given a weighted directed graph with nnn nodes and mmm edges. Node SSS is marked as the source node and each edge has a positive weight. So the shortest path from source to each node is defined(shortest path to nodes which are not reachable from the source node is also considered defined and cost of shortest path to those nodes is infinity). But you want to make it undefined. Shortest path from one node to another is undefined if you can make the cost of the shortest path arbitrarily small.

This is a companion discussion topic for the original entry at