We determine the average number ϑ(N,K), of \textit{NK}-Kauffman
networks that give rise to the same binary function. We show that, for N≫1, there exists a connectivity critical value Kc such that ϑ(N,K)≈eϕN (ϕ>0) for K<Kc and
ϑ(N,K)≈1 for K>Kc. We find that Kc is not a
constant, but scales very slowly with N, as Kc≈log2log2(2N/ln2). The problem of genetic robustness emerges as a statistical property
of the ensemble of \textit{NK}-Kauffman networks and impose tight constraints
in the average number of epistatic interactions that the genotype-phenotype map
can have.Comment: 4 figures 18 page