LineGraph

The graph whose vertices are the edges of g, joined when the original edges share an endpoint.

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

LineGraph(g)one vertex per edge of g (numbered 1..EdgeCount(g), in EdgeList order), UNDIRECTED regardless of g's own edge directions.

Typed signatures

Type	Package	Applies
(value) -> value	combinatorics	always

Domain: Collections

Details

• EdgeCount(LineGraph(g)) = sum over v of C(VertexDegree(v), 2) for a simple g -- every pair of edges sharing vertex v contributes one line-graph edge.

Examples

Basic #

live ↗

In$\mathrm{EdgeCount}(\mathrm{LineGraph}(\mathrm{CompleteGraph}(3)))$Out$3$

About

Examples	1
Checked against	Wolfram Language 1 agreeSageMath 1 agree
Crosswalk	Wolfram Language

Implementation

mappedsagepackages/oracle/src/mappings.ts

See also: VertexDegree, AdjacencyGraph