Editing Spanning tree (section)

{{Short description|Tree which includes all vertices of a graph}}
{{About||the network protocol|Spanning Tree Protocol|other uses|}}
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[[File:4x4 grid spanning tree.svg|thumb|A spanning tree (blue heavy edges) of a [[grid graph]]]]
In the [[mathematics|mathematical]] field of [[graph theory]], a '''spanning tree''' ''T'' of an [[undirected graph]] ''G'' is a subgraph that is a [[tree (graph theory)|tree]] which includes all of the [[Vertex (graph theory)|vertices]] of ''G''.<ref name="NetworkX 2.6.2 documentation">{{citation | title=Tree | website=NetworkX 2.6.2 documentation | url=https://networkx.org/documentation/stable/reference/algorithms/tree.html | access-date=2021-12-10 | quote=For trees and arborescence, the adjective “spanning” may be added to designate that the graph, when considered as a forest/branching, consists of a single tree/arborescence that includes all nodes in the graph. }}</ref> In general, a graph may have several spanning trees, but a graph that is not [[connected graph|connected]] will not contain a spanning tree (see about [[#Spanning forests|spanning forests]] below). If all of the [[edge (graph theory)|edges]] of ''G'' are also edges of a spanning tree ''T'' of ''G'', then ''G'' is a tree and is identical to ''T'' (that is, a tree has a unique spanning tree and it is itself).