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One potential algorithm is to first find strongly connected components of the given graph G (http://en.wikipedia.org/wiki/Strongly_connected_component). All the nodes of a single SCC must have the same value of number of nodes reachable. So consider the condensation of G which is a DAG. and obtain the number of reachable nodes from each node in this DAG (perhaps by doing modified breadth-first-search traversals starting from nodes with no incoming edges).
Currently the code performs a new Breadth-first-search for every node. Improve its performance.
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