Scale-Free Networks: Characteristics of the Time-Variant Robustness and Vulnerability

In order to study the change trend of the survivability of complex networks over time, a new method is proposed to measure the survivability of the scale-free networks. The concepts of robust and vulnerable dynamic angles are introduced to visually reflect the characteristics of the time-variant robustness and vulnerability when the heterogeneity of degree distribution increases or decreases. Then, the global container shipping network and the product copurchasing network are discussed as examples, respectively. Main results point to that when the degree distribution of a scale-free network becomes more heterogeneous over time, the robustness will enhance and the vulnerability will aggravate gradually. On the contrary, when the degree distribution becomes less heterogeneous, the robustness will reduce and the vulnerability will mitigate. The above-mentioned two indicators change in a reverse trend and the change speeds are different. The results of this article are an important theoretical exploration and advance of analytical methods to shed light on the dynamic mechanism and evolution trend of the scale-free network's survivability.