Why is the node with the greatest DFS post-order number not necessarily a sink? A sink in a directed graph is a node with no outgoing edges. If I perform a depth first search, why is it that the node with the least post-order number (and thus the highest pre-order number) not necessarily a sink - isn't this node found last?

Also, intuitively, the node with the greatest post-order number should be a source - a node with no incoming edges.
If your graph is strongly connected, there is no sink, so I guess that answers your question...