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  "body": "\n## Summary\n\nIn graph theory, a branch of mathematics, a **cluster graph** is a [[graph|00C0BR7D7H]] formed from the disjoint union of [[complete graphs|03WKB2H474]]. Equivalently, a graph is a cluster graph if and only if it has no three-vertex induced path; for this reason, the cluster graphs are also called **$P_{3}$-free graphs**. They are the [[complement graphs|0MCYJ72VGA]] of the complete multipartite graphs and the 2-leaf powers. The cluster graphs are [[transitively closed|05J9NWX07X]], and every transitively closed undirected graph is a cluster graph.\n",
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