We determine the average number Ο(N,K), of \textit{NK}-Kauffman
networks that give rise to the same binary function. We show that, for Nβ«1, there exists a connectivity critical value Kcβ such that Ο(N,K)βeΟN (Ο>0) for K<Kcβ and
Ο(N,K)β1 for K>Kcβ. We find that Kcβ is not a
constant, but scales very slowly with N, as Kcββlog2βlog2β(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