Repairing a failed clustered network by external activation

Many real-world systems inherently exhibit complex network structures, requiring specific strategies or mechanisms to restore functionality in the event of failures. However, previous research on network repair has often overlooked the influence of clustering, which is prevalent in real-world complex systems and plays a crucial role in shaping local connectivity. In this study, an external activating strategy is employed to examine the repair mechanisms of clustered networks. It is demonstrated that the presence of clustering significantly enhances the network’s average activity X¯ after repair through three distinct dynamical processes. The findings indicate that as the fraction r of randomly selected nodes increases, the repaired network exhibits three states: functional (complete repair), inactive (incomplete repair), and bistable switching between the two states, divided by the critical points r1 and r2. We also find that as the clustering coefficient c increases, an increase in functional states and a decrease in inactive states can be observed in brain and cellular dynamics, whereas the opposite occurs in spin dynamics. This results in changes to r1 and r2 at different c. Furthermore, we find that a linear scaling relationship exists between these thresholds and the clustering coefficient c. These findings enhance the understanding of repair mechanisms in clustered networks and provide valuable insights for designing systems with improved resilience.