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Network robustness against attacks has been widely studied in fields asdiverse as the Internet, power grids and human societies. Typically, in thesestudies, robustness is assessed only in terms of the connectivity of the nodesunaffected by the attack. Here we put forward the idea that the connectivity ofthe affected nodes can play a crucial role in properly evaluating the overallnetwork robustness and its future recovery from the attack. Specifically, wepropose a dual perspective approach wherein at any instant in the networkevolution under attack, two distinct networks are defined: (i) the ActiveNetwork (AN) composed of the unaffected nodes and (ii) the Idle Network (IN)composed of the affected nodes. The proposed robustness metric considers boththe efficiency of destroying the AN and the efficiency of building-up the IN.We show, via analysis of both prototype networks and real world data, thattrade-offs between the efficiency of Active and Idle network dynamics give riseto surprising crossovers and re-ranking of different attack strategies,pointing to significant implications for decision making.

Network robustness assessed within a dual connectivity perspective