Interplay of mutation and disassortativity.

Despite disassortativity being commonly observed in many biological networks, our current understanding of its evolutionary origin is inadequate. Motivated by the occurrence of mutations during an evolutionary time span that results in changes in the behavior of interactions, we demonstrate that if we maximize the stability of the underlying system, the genetic algorithm leads to the evolution of a disassortative structure. The mutation probability governs the degree of saturation of the disassortativity coefficient, and this reveals the origin of the wide range of disassortativity values found in real systems. We analytically verify these results for star networks, and by considering various values for the antisymmetric couplings, we find a regime in which scale-free networks are more stable than the corresponding random networks.