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

Synopsis

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

See also

Ways to use lineGraph :

For the programmer

The object lineGraph is a method function.