Editing Complement graph (section)

{{short description|Graph with same nodes but opposite connections as another}}
[[File:Petersen graph complement.svg|thumb|upright=1.35|The [[Petersen graph]] (on the left) and its complement graph (on the right).]]

In the [[mathematical]] field of [[graph theory]], the '''complement''' or '''inverse''' of a [[Graph (discrete mathematics)|graph]] {{mvar|G}} is a graph {{mvar|H}} on the same [[Vertex (graph theory)|vertices]] such that two distinct vertices of {{mvar|H}} are adjacent [[if and only if]] they are not adjacent in {{mvar|G}}. That is, to generate the complement of a graph, one fills in all the missing [[Edge (graph theory)|edges]] required to form a [[complete graph]], and removes all the edges that were previously there.<ref name="bm">{{citation
 | last1=Bondy
 | first1=John Adrian
 | authorlink1=John Adrian Bondy
 | last2=Murty
 | first2=U. S. R.
 | authorlink2=U. S. R. Murty
 | title=Graph Theory with Applications
 | year=1976
 | publisher=North-Holland
 | isbn=0-444-19451-7
 | url=https://archive.org/details/graphtheorywitha0000bond/page/6
 | page=[https://archive.org/details/graphtheorywitha0000bond/page/6 6]
 }}.</ref> 

The complement is not the [[complement (set theory)|set complement]] of the graph; only the edges are complemented.