  The scale-fee networks, having connectivity distribution $P(k)\sim
k^{-\alpha}$ (where $k$ is the site connectivity), is very resilient to random
failures but fragile to intentional attack. The purpose of this paper is to
find the network design guideline which can make the robustness of the network
to both random failures and intentional attack maximum while keeping the
average connectivity $<k>$ per node constant. We find that when $<k>=3$ the
robustness of the scale-free networks reach its maximum value if the minimal
connectivity $m=1$, but when $<k>$ is larger than four, the networks will
become more robust to random failures and targeted attacks as the minimal
connectivity $m$ gets larger.

Statistical Mechanics;Other Condensed Matter