Choice of the core point in the set 𝒜 , based on  (Subscript[It, 0]) random choices

Input: data set 𝒜 ⊂ (ℝ^n), ϵ > 0, number of random choices (Subscript[It, 0]);
Output: core point (Subscript[c, p]), number of points |(Subscript[C, p])| in ϵ-neighborhood of the core point (Subscript[c, p]);
Submodules: none needed

CorePoint[A_,eps_,It0_]:=Module[{kk=1,rc,Ne,B,br,br1,rep,Rep},
rc=RandomChoice[A]; Ne=Neps[A,rc,eps]; br=Length[Ne];
(* rep - chosen point; Rep -  number of points in the neighborhood of point rep *)
rep=rc;Rep=Ne;kk=1;B=Complement[A,{rc}];
While[kk<It0,kk=kk+1;
rc=RandomChoice[B];Ne=Neps[B,rc,eps]; br1=Length[Ne];
If[br1>br, br=br1;rep=rc;Rep=Ne]
	];
{rep,Length[Rep]}
]