The parameters hare are n and r, the first one is the number of vertices and the second is the degree of each vertex. The program will work, however, for any sequence d, the only thing you will need to type this sequence manually.

r=3;(*the degree of each vertex*)
n=50; (*number of vertices*)

d=Table[r,{n}];

GraphPlot[
Flatten [
Partition[
RandomSample[Flatten @ Table[Table[i,{j,1,d[[i]]}],{i,1,Length[d]}]],2]/.{x_,y_}->{x->y}],
VertexLabeling->True
]