  Most current studies estimate the invulnerability of complex networks using a
qualitative method that analyzes the inaccurate decay rate of network
efficiency. This method results in confusion over the invulnerability of
various types of complex networks. By normalizing network efficiency and
defining a baseline, this paper defines the invulnerability index as the
integral of the difference between the normalized network efficiency curve and
the baseline. This quantitative method seeks to establish a benchmark for the
robustness and fragility of networks and to measure network invulnerability
under both edge and node attacks. To validate the reliability of the proposed
method, three small-world networks were selected as test beds. The simulation
results indicate that the proposed invulnerability index can effectively and
accurately quantify network resilience. The index should provide a valuable
reference for determining network invulnerability in future research.
