Counting the number of shortest paths through a node in a DAG?

You could use a breadth first search for each pair of Src/Dest nodes and see which of those have your given node in the path. You would have to modify the search slightly such that once you've found your shortest path, you continue to empty the queue until you reach a path that causes you to increase the size. In this way you're not bound by random chance if there are multiple shortest paths.

This is only an option with non-weighted graphs, of course.

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