Optimal wiring principle and plateaus in the degree of separation for cortical neurons

Scaling properties of a cortical network wired in a stochastic manner with a distance-dependent probability of a direct connection are considered. In the infinite network limit, an average degree of separation between neurons displays both universality and criticality. The latter feature manifests itself by appearance of a stairlike structure with numerous plateaus as a function of a connectivity exponent. It is suggested that these plateaus may be advantageous in the cortex design. Wiring principle incorporating minimization of both axonal length and the degree of separation is also discussed. This principle leads naturally to a trade-off between saving axons and saving energy required in the communication.