IsCompleteGraph

Whether a Graph is complete — every pair of vertices joined by an edge.

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

IsCompleteGraph(g)true iff g is simple (no self-loop, no parallel edge) and every ORDERED pair of distinct vertices is joined.

Typed signatures

Type	Package	Applies
(value) -> boolean	combinatorics	always

Domain: Collections

Details

• Wolfram calls this CompleteGraphQ; this library uses the Is… spelling everywhere.
• A directed graph counts too, kernel-verified against Wolfram 15: CompleteGraphQ(Graph({1->2, 2->1})) is True, and CompleteGraph(3, DirectedEdges->True) (every ordered pair, both directions) is complete. An undirected edge covers BOTH ordered pairs between its endpoints; a directed edge covers only the one it points.

Examples

Basic #

live ↗

In$\mathrm{IsCompleteGraph}(\mathrm{CompleteGraph}(5))$Out$\mathrm{True}$

live ↗

In$\mathrm{IsCompleteGraph}(\mathrm{Graph}(\bigl\lbrack1, 2, 3\bigr\rbrack, \bigl\lbrack\mathrm{UndirectedEdge}(1, 2), \mathrm{UndirectedEdge}(2, 3)\bigr\rbrack))$Out$\mathrm{False}$

live ↗

In$\mathrm{IsCompleteGraph}(\mathrm{Graph}(\bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack\mathrm{DirectedEdge}(1, 2), \mathrm{DirectedEdge}(2, 1)\bigr\rbrack))$Out$\mathrm{True}$

About

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

Implementation

mappedsagepackages/oracle/src/mappings.ts

See also: CompleteGraph, IsSimpleGraph