Six Degrees of Separation in Boolean Function Networks with Neutrality

Abstract. We analyze two Boolean function networks with different degrees of neutrality. The results show that the one with explicit neutrality is a small-world network where each pair of possible solutions has a short distance and most of the possible solutions are highly clustered. These network structural properties owe their existence to the “short cuts” introduced by redundant genes in the genotypes. We explain some important small-world network structures, such as clusters, hubs and power law link distribution. These properties have potential to be useful in designing efficient evolutionary algorithms to navigate search in the network.