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Random regular graph
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<p>A random <i>r</i>-regular graph is a <a href="/facts/Graph_(discrete_mathematics)/kw3eIBUe">graph</a> selected from G n , r {\displaystyle {\mathcal {G}}_{n,r}} , which denotes the probability space of all <a href="/facts/Regular_graph/j9dSoLE6"><i>r</i>-regular graphs</a> on n {\displaystyle n} vertices, where 3 ≤ r < n {\displaystyle 3\leq r<n} and n r {\displaystyle nr} is even. It is therefore a particular kind of <a href="/facts/Random_graph/gfQhq1Sz">random graph</a>, but the regularity restriction significantly alters the properties that will hold, since most graphs are not regular. </p>