Network robustness assessed within a dual connectivity framework: joint dynamics of the Active and Idle Networks.

Network robustness against attacks has been widely studied in fields as diverse as the Internet, power grids and human societies. But current definition of robustness is only accounting for half of the story: the connectivity of the nodes unaffected by the attack. Here we propose a new framework to assess network robustness, wherein the connectivity of the affected nodes is also taken into consideration, acknowledging that it plays a crucial role in properly evaluating the overall network robustness in terms of its future recovery from the attack. Specifically, we propose a dual perspective approach wherein at any instant in the network evolution under attack, two distinct networks are defined: (i) the Active Network (AN) composed of the unaffected nodes and (ii) the Idle Network (IN) composed of the affected nodes. The proposed robustness metric considers both the efficiency of destroying the AN and that of building-up the IN. We show, via analysis of well-known prototype networks and real world data, that trade-offs between the efficiency of Active and Idle Network dynamics give rise to surprising robustness crossovers and re-rankings, which can have significant implications for decision making.