Editing Minimum spanning tree (section)

===Cycle property===
''For any cycle {{mvar|C}} in the graph, if the weight of an edge {{mvar|e}} of {{mvar|C}} is larger than any of the individual weights of all other edges of {{mvar|C}}, then this edge cannot belong to an MST.''

Proof: [[Proof by contradiction|Assume the contrary]], i.e. that {{mvar|e}} belongs to an MST {{math|''T''{{sub|1}}}}. Then deleting {{mvar|e}} will break {{math|''T''{{sub|1}}}} into two subtrees with the two ends of {{mvar|e}} in different subtrees. The remainder of {{mvar|C}} reconnects the subtrees, hence there is an edge {{mvar|f}} of {{mvar|C}} with ends in different subtrees, i.e., it reconnects the subtrees into a tree {{math|''T''{{sub|2}}}} with weight less than that of {{math|''T''{{sub|1}}}}, because the weight of {{mvar|f}} is less than the weight of {{mvar|e}}.