Mathematics — Graph Theory · line-graph-multigraph
Problem
Let G=(V,E,φ) be a multigraph. The line graph L(G) is defined as the simple graph (E,F), where
F={{e1,e2}∈P2(E)∣φ(e1)∩φ(e2)=∅}.
(In other words, L(G) is the graph whose vertices are the edges of G, and in which two vertices e1 and e2 are adjacent if and only if the edges e1 and e2 of G share a common endpoint.)