Editing Line graph (section)

===Line digraphs{{anchor|Line digraph}}===
[[File:DeBruijn-as-line-digraph.svg|thumb|360px|Construction of the [[de Bruijn graph]]s as iterated line digraphs]]
It is also possible to generalize line graphs to directed graphs.{{sfnp|Harary|Norman|1960}} If {{mvar|G}} is a directed graph, its '''directed line graph''' or '''line digraph''' has one vertex for each edge of {{mvar|G}}. Two vertices representing directed edges from {{mvar|u}} to {{mvar|v}} and from {{mvar|w}} to {{mvar|x}} in {{mvar|G}} are connected by an edge from {{mvar|uv}} to {{mvar|wx}} in the line digraph when {{math|1=''v'' = ''w''}}. That is, each edge in the line digraph of {{mvar|G}} represents a length-two directed path in {{mvar|G}}.  The [[de Bruijn graph]]s may be formed by repeating this process of forming directed line graphs, starting from a [[complete graph|complete directed graph]].{{sfnp|Zhang|Lin|1987}}