On the Predictability of Network Robustness from Spectral Measures

Robustness against failure and attack is one of the essential properties of large-scale dynamical system such as power grids, transportation system, communication systems, and computer networks. Despite its popularity and intuitiveness, a major drawback of descriptive robustness metrics such as the size of the largest connected component and the diameter is its computational complexity. On the contrary, predictive metrics such as the spectral radius, the natural connectivity, and the algebraic connectivity are much easier to obtain than descriptive metrics, but the predictability of those measures against different levels and types of failures/attacks has not been well understood. In this paper, we therefore investigate how effectively predictive metrics (spectral measures) can estimate the robustness of a network against random node removal. Our finding includes that, among five types of spectral measures, the effective resistance is most suitable for predicting the largest cluster component size under low node removal ratio, and that the predictability of the effective resistance is stable for various networks generated with different network generation models.