As communication and network technology has advanced into all areas of human life, large-scale failures of such infrastructures can have a drastic impact on its users, the economy and society in general. Significant attention has been paid to study and improve the dependability of such systems, intending to augment their resilience against challenges. This paper presents a computational approach for a multi-level multi-dimensional study of network robustness, providing hard performance guarantees for networks and helping to assess risk and uncertainty associated with threats. We demonstrate in a case study that such approach is well suited to understood the root causes and subsequent effects of network challenges and therefore obtain deeper insights into the resilience of a network under stress.