  In recent years, many network perturbation techniques, such as topological
perturbations and service perturbations, were employed to study and improve the
robustness of complex networks. However, there is no general way to evaluate
the network robustness. In this paper, we propose a new global measure for a
network, the reconstructability coefficient {\theta}, defined as the maximum
number of eigenvalues that can be removed, subject to the condition that the
adjacency matrix can be reconstructed exactly. Our main finding is that a
linear scaling law, E[{\theta}]=aN, seems universal, in that it holds for all
networks that we have studied.
