A random r-regular graph is a graph selected from G n , r {\displaystyle {\mathcal {G}}_{n,r}} , which denotes the probability space of all r-regular graphs 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 random graph, but the regularity restriction significantly alters the properties that will hold, since most graphs are not regular.
A random r-regular graph is a graph selected from G n , r {\displaystyle {\mathcal {G}}_{n,r}} , which denotes the probability space of all r-regular graphs 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 random graph, but the regularity restriction significantly alters the properties that will hold, since most graphs are not regular.
Source: Wikipedia "Random regular graph" · CC BY-SA 4.0
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