Relationship between fragility and resilience in complex networks

While the impacts of fragility and resilience on the networked system have attracted a lot of attention, theoretical analyses of the relationship between fragility and resilience are still lacking. In this paper, we explain from a mathematical perspective that when the network is attacked, the fragility will increase and the resilience will decrease. In addition, we provide analytical and numerical supporting evidence for the relationship that fragility and resilience of complex networks subject to a linear negative correlation in double logarithmic coordinates. This means that the impact of external attacks on system’s resilience performance is heavier than that on fragility.