In the first step, PE assigns the indices formula_9 to the local vertices in formula_10. These vertices in formula_10 are removed, together with their corresponding outgoing edges. For each outgoing edge formula_12 with endpoint in another PE formula_13, the message formula_12 is posted to PE . After all vertices in formula_10 are removed, the posted messages are sent to their corresponding PE. Each message formula_12 received updates the indegree of the local vertex . If the indegree drops to zero, is added to formula_17. Then the next iteration starts.