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  "body": "\n## Summary\n\nIn graph theory, **toughness** is a measure of the connectivity of a graph. A graph $G$ is said to be $t$-tough for a given [[real number|08J2M1JYAG]] $t$ if, for every [[integer|0C4JS9RF5M]] $k \u003e 1$, $G$ cannot be split into $k$ different connected components by the removal of fewer than $tk$ vertices. For instance, a graph is $1$-tough if the number of components formed by removing a set of vertices is always at most as large as the number of removed vertices. The toughness of a graph is the maximum $t$ for which it is $t$-tough; this is a finite number for all finite graphs except the [[complete graphs|03WKB2H474]], which by convention have infinite toughness.\n",
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