Two-Peak and Three-Peak Optimal Complex Networks

The problem of designing networks to be robust against random failures and deliberate attacks was analyzed. A constructive proof of robust network architecture was obtained. Networks with a power-law node connectivity distribution were found to be fragile to targeted attacks but robust to random failures. Networks with an exponentially decaying connectivity distribution were more resilient to attacks and less tolerant to failures. It was shown that the optical network configuration that maximize the percolation threshold under attack and/or random failures possesses at the most three distinct node degrees.