IsAcyclicGraph

Whether a Graph contains no cycle.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageAcyclicGraphQ✓

IsAcyclicGraph(g)true iff g has no cycle, respecting edge direction where g has directed edges.

Typed signatures

Type	Package	Applies
`(value) -> boolean`	`combinatorics`	always

Domain: Collections

Details

Wolfram calls this AcyclicGraphQ; this library uses the Is… spelling everywhere.
A self-loop, and two vertices joined by directed edges in BOTH directions, both count as cycles. An undirected edge alone never does -- walking straight back over the SAME edge you just arrived by isn't a cycle, so a plain undirected tree reads acyclic (matches IsTreeGraph's own edges = vertices - 1 check).

Examples

Basic #

\mathrm{IsAcyclicGraph}(\mathrm{Graph}(\bigl\lbrack1, 2, 3, 4\bigr\rbrack, \bigl\lbrack\mathrm{UndirectedEdge}(1, 2), \mathrm{UndirectedEdge}(2, 3), \mathrm{UndirectedEdge}(3, 4)\bigr\rbrack))

Out

\mathrm{True}

\mathrm{IsAcyclicGraph}(\mathrm{CycleGraph}(4))

Out

\mathrm{False}

\mathrm{IsAcyclicGraph}(\mathrm{Graph}(\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack\mathrm{DirectedEdge}(1, 2), \mathrm{DirectedEdge}(2, 1)\bigr\rbrack))

Out

\mathrm{False}

About

Examples	3
Checked against	Wolfram Language 3 agreeSageMath 3 agree
Crosswalk	Wolfram Language

mappedsagepackages/oracle/src/mappings.ts