lineGraph -- Returns the line graph of an undirected graph

Usage:

L = lineGraph G
Inputs:
- G, a graph,
Outputs:
- L, a graph, The line graph of G

Description

The line graph L of an undirected graph G is the graph whose vertex set is the edge set of the original graph G and in which two vertices are adjacent if their corresponding edges share a common endpoint in G.

i1 : G = graph({{1,2},{2,3},{3,4},{4,1},{1,3},{4,2}},EntryMode=>"edges")

o1 = Graph{1 => {2, 3, 4}}
           2 => {1, 3, 4}
           3 => {1, 2, 4}
           4 => {1, 2, 3}

o1 : Graph

i2 : lineGraph G

o2 = Graph{set {1, 2} => {set {1, 3}, set {4, 1}, set {2, 3}, set {4, 2}}}
           set {1, 3} => {set {1, 2}, set {4, 1}, set {2, 3}, set {4, 3}}
           set {2, 3} => {set {1, 2}, set {1, 3}, set {4, 2}, set {4, 3}}
           set {4, 1} => {set {1, 2}, set {1, 3}, set {4, 2}, set {4, 3}}
           set {4, 2} => {set {1, 2}, set {4, 1}, set {2, 3}, set {4, 3}}
           set {4, 3} => {set {1, 3}, set {4, 1}, set {2, 3}, set {4, 2}}

o2 : Graph

Ways to use lineGraph:

lineGraph(Graph)

For the programmer

The object lineGraph is a method function.

The source of this document is in Graphs.m2:2335:0.