# lineGraph -- returns the line graph of a (hyper)graph

## Synopsis

• Usage:
L = lineGraph H
• Inputs:
• H, ,
• Outputs:
• L, , the line graph of H

## Description

The line graph L of a hypergraph H has a vertex for each edge in H. Two vertices in L are adjacent if their edges in H share a vertex. The order of the vertices in L are determined by the implicit order on the edges of H. See edges.

 i1 : R = QQ[a..e]; i2 : G = graph {a*b,a*c,a*d,d*e} o2 = Graph{edges => {{a, b}, {a, c}, {a, d}, {d, e}}} ring => R vertices => {a, b, c, d, e} o2 : Graph i3 : lineGraph G o3 = Graph{edges => {{x , x }, {x , x }, {x , x }, {x , x }}} 0 1 0 2 1 2 2 3 ring => QQ[x ..x ] 0 3 vertices => {x , x , x , x } 0 1 2 3 o3 : Graph