A random regular graph is a regular graph sampled according to a specified probability law.
The uniform simple labelled model chooses among all simple 
-regular graphs on 
, for 
and even 
. Every graph in that finite set has equal probability. The
law need not be conditioned on connectedness or on the absence of bipartite
graphs. Its adjacency matrix has the Kesten-McKay
distribution as its limiting empirical spectral law for fixed 
.
Random Regular Graph
See also
Graph Spectrum, Kesten-McKay Distribution, Random Graph, Regular GraphExplore with Wolfram|Alpha
References
He, Y.; Huang, J.; and Wang, X. "Bulk Universality of Random Regular Graphs." 6 Oct 2026. https://arxiv.org/abs/2610.08127.Cite this as:
Weisstein, Eric W. "Random Regular Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RandomRegularGraph.html