Graphs: isCyclic Digraph sometimes fails to detect cycles

[taboege]

The Graphs package has a method isCyclic to detect whether a Digraph contains a directed cycle. It often works:

isCyclic digraph({{1,2},{2,3},{3,1}}) --> true (correct)
isCyclic digraph({{1,2},{2,3},{3,4},{4,3}}) --> true (correct)
isCyclic digraph({{1,2},{2,3},{3,4},{2,4},{3,4}}) --> false (correct)

But on other small examples, it fails, reporting a graph as acyclic when it has a cycle

isCyclic digraph({{1,3},{1,4},{2,4},{3,2},{4,3}}) --> false (incorrect: 2 -> 4 -> 3 -> 2)

[taboege]

The implementation of isCyclic currently relies on depthFirstSearch which records a discovery time and a finishing time for each vertex. However, these numbers cannot distinguish between a cyclic and an acyclic graph:

E = {{1,3},{1,4},{3,2},{4,3}};
-- The two hash tables are equal:
print depthFirstSearch(digraph(E)); -- acyclic
print depthFirstSearch(digraph(E|{{2,4}})); -- cyclic

Here, the edge {2,4} creates a cycle but because of the (chance) order in which DFS visits the nodes (in my case 1 -> 4 -> 3 -> 2), that edge has no influence on the discovery and finishing times. Cycle detection has to happen during the DFS traversal.

The topologicalSort implementation actually contains all the gears to detect cycles. I'll post a pull request which uses that instead of DFS.