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Spread velocity, epidemic threshold, and infection density at steady state are three non-negligible features describing the spread of epidemics. Combining these three features together, a new network robustness metric with respect to epidemics was proposed in this paper. The real-time robustness of the network was defined and analyzed. By using the susceptible–infected (SI) and susceptible–infected–susceptible (SIS) epidemic models, the robustness of different networks was analyzed based on the proposed network robustness metric. The simulation results showed that homogeneous networks present stronger robustness than do heterogeneous networks at the early stage of the epidemic, and the robustness of the heterogeneous networks becomes stronger than that of the homogeneous ones with the progress of the epidemic. Moreover, the irregularity of the degree distribution decreases the network robustness in homogeneous networks. The network becomes more vulnerable as the average degree grows in both homogeneous and heterogeneous networks.

A Novel Metric to Quantify the Real-Time Robustness of Complex Networks With Respect to Epidemic Models