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  "body": "\n## Summary\n\nA **random *r*-regular graph** is a [[graph|00C0BR7D7H]] selected from $\\mathcal{G}_{n,r}$, which denotes the [[probability space|0NFPJVJJHX]] of all [[*r*-regular graphs|0KA4S8R39M]] on $n$ vertices, where $3 \\le r \u003c n$ and $nr$ is even. It is therefore a particular kind of random graph, but the regularity restriction significantly alters the properties that will hold, since most graphs are not regular.\n",
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