  It has been found that the networks with scale-free distribution are very
resilient to random failures. The purpose of this work is to determine the
network design guideline which maximize the network robustness to random
failures with the average number of links per node of the network is constant.
The optimal value of the distribution exponent and the minimum connectivity to
different network size are given in this paper. Finally, the optimization
strategy how to improve the evolving network robustness is given.
