Explains a directed graph and a cycle in it
A directed graph is a set of nodes and edges each with a direction; a cycle is a path following the directions that returns to its start. A prerequisite structure must have none, since a cycle makes every knobit on it imply the others.
Can AI do this?
Not settled yet The benchmark tested this, but the models' answers do not settle yet whether they master it. 0 of 4 models in the current benchmark master it.
| Model | Tier | Probability of mastery | Status |
|---|---|---|---|
| gemini-4-argon | Flagship | 99% | Not shown |
| gemini-3.5-flash-lite | Low cost | 98% | Not shown |
| gpt-6-luna | Low cost | 98% | Not shown |
| claude-haiku-5-5 | Low cost | 99% | Not shown |
Mastered means a probability of at least 90% that the model has this knobit, estimated from its graded answers. “Not shown” means the answers do not settle it either way. How the models are tested.
What it looks like in practice
Expected result: A cycle found in, or ruled out of, a small directed graph, with why a prerequisite graph must be acyclic
How it is assessed: Finds a cycle in a given directed graph or states that there is none, following edge directions
Related knobits
Builds on
Needed for
- T-105 Recognises a cycle in the mastery implications
- T-152 Explains mastery implication in a knobit graph
All 16 knobits of Review a knobit register for assessment.
Source: Part B candidate of k12-dmbok for activity TO-1 (a need for school knowledge no knobit of the activity reached), accepted by Peep Küngas on 31 Oct 2026