An interactive DAG. Eleven things you can do to a one-way graph — and one you can’t.
EncounterThe arrows point one way. Each edge is a door that locks behind you.
The line never falls. Acyclicity is bought — this is the price you didn’t pay.
width
4
depth
8 nodes
critical path
23 time
ready now
1
left
11
legal orders
24
width is breath; depth is fate.
Circular dependency — the cycle was always there.
Refused.
You amputated this edge to make the graph run.
Panel
Footnotes for the math-curious
Frontier = the unfinished nodes with in-degree 0 — Kahn’s algorithm, made visible.
Width = largest antichain = fewest chains that cover the graph — Dilworth’s theorem (computed here by bipartite matching on the reachability relation).
Depth = longest path = the critical path; more workers can’t shorten it.
“Use” lights a node’s transitive closure: every descendant it can reach.
This graph admits exactly 24 legal topological orders; the back-edge verify → design would leave zero.
You performed eleven verbs and were refused the twelfth.
You only ever held the frontier. The cycle was always there; acyclicity is what you bought to be rid of it.