Fig. 1.

An illustration of how to calculate the structural consistency. In the first plot, the blue dashed links constitute the perturbation set $\mathrm{\Delta }E=\left\{\left(\mathrm{5,8}\right),\left(\mathrm{6,9}\right)\right\}$ (corresponding to $\mathrm{\Delta }A$), while the solid links constitute the set $E^R$ (corresponding to $A^R$). The second plot shows the adjacency matrix A of the given network, where the number in each square is the corresponding value of the matrix element. The black and blue squares represent the links in $E^R$ and $\mathrm{\Delta }E$, respectively. To calculate the consistency, we perturb $A^R$ with $\mathrm{\Delta }A$. The perturbed matrix $\tilde{A}$ is shown in the third plot, from which we derive the perturbed network in the fourth plot, where the red dashed lines are outcome links selected by ranking all links in $U-E^R$ in descending order according to their corresponding values in $\tilde{A}$. Since there are two links in $\mathrm{\Delta }E$, then $L=2$, and the set $E^L=\left\{\left(\mathrm{3,8}\right),\left(\mathrm{6,9}\right)\right\}$. In this case, only one of the two blue links is recovered by perturbation; then we have ${\sigma }_c=0.5$.