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  "body": "\n## Summary\n\nIn mathematics, the **commuting graph** of a [[semigroup|0XMEM406JM]], or in particular of a group, is an undirected graph in which the vertices are elements of the semigroup and there is an edge between any pair of elements that [[commute|099E72KTF8]] (that is, there is an edge between vertices $x$ and $y$ if and only if $xy=yx$ in the semigroup). Commuting graphs have been used to study groups and semigroups by seeking relationships between the combinatorial structure of the graph and the algebraic structure of the group or semigroup.\n",
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        "what": "edge defines in",
        "note": "at least one definition",
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        "what": "edge instance_of in",
        "note": "at least two examples",
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        "what": "edge not_instance_of in",
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        "what": "edge specializes both",
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