Fig. 1.

(A and B) Agents i and $\widehat{i}$ have thresholds ${\tau }_i=1/3$ and ${\tau }_{\widehat{i}}=1/2$, but because an extra A-neighbor has been added to $\widehat{i}$, they are dynamically equivalent. (C) To ensure that the added node does not switch, two B neighbors are added who also will not switch, forming a V-block.