Self-organized criticality and structural robustness: Node-failure analysis of the sandpile model on rewired networks

Self-Organized Criticality (SOC) provides a useful framework for understanding how complex systems maintain critical behavior through local interactions, yet its robustness to structural damage remains insufficiently understood. In this work, we investigate the impact of node failures on the Bak–Tang–Wiesenfeld sandpile model implemented on rewired network topologies. Starting from a regular lattice, we introduce a degree-preserving rewiring procedure that progressively transforms the structure while retaining the basic sandpile dynamics, and we then apply random node removal to analyze the degradation of system performance. Across a broad range of rewiring and node-removal levels, we quantify avalanche-duration statistics, grain density, grain movements, graph size, giant-cluster size, and open-cluster formation. The results reveal a strong topological effect on robustness. Regular grids preserve broad avalanche activity and transport only up to about 40% node removal, after which fragmentation rapidly suppresses large avalanches and degrades dynamical performance. In contrast, rewired networks retain a dominant open component and sustained grain transport up to about 60% node removal before undergoing abrupt collapse. This increased robustness is associated with shorter effective paths to dissipative boundaries, delayed fragmentation, and a more gradual deterioration of the main dynamical indicators. Overall, the results show that modest topological randomization can substantially enhance the structural robustness of sandpile dynamics under node removal, while the proposed framework provides a simple setting for studying resilience and tipping behavior in networked nonlinear systems.