Enhanced robustness of single-layer networks with redundant dependencies

Abstract

Dependency links in single-layer networks offer a convenient way of modeling nonlocal percolation effects in networked systems where certain pairs of nodes are only able to function together. We study the percolation properties of the weak variant of this model: nodes with dependency neighbours may continue to function if at least one of their dependency neighbours is active. We show that this relaxation of the dependency rule allows for more robust structures and a rich variety of critical phenomena, as percolation is not determined strictly by finite dependency clusters. We study Erdös-Rényi and random scale-free networks with an underlying Erdös-Rényi network of dependency links. We identify a special "cusp" point above which the system is always stable, irrespective of the density of dependency links. We find continuous and discontinuous hybrid percolation transitions, separated by a tricritical point for Erdös-Rényi networks. For scale-free networks with a finite degree cutoff we observe the appearance of a critical point and corresponding double transitions in a certain range of the degree distribution exponent. We show that at a special point in the parameter space, where the critical point emerges, the giant viable cluster has the unusual critical singularity $S-S_c\propto (p-p_c{)}^{1/4}$. We study the robustness of networks where connectivity degrees and dependency degrees are correlated and find that scale-free networks are able to retain their high resilience for strong enough positive correlation, i.e., when hubs are protected by greater redundancy.

arXiv comment18 pages, 10 figures

References in corpus (18)

• Catastrophic cascade of failures in interdependent networks
• The structure and dynamics of multilayer networks
• k-core organization of complex networks
• Avalanche Collapse of Interdependent Network
• The critical effect of dependency groups on the function of networks
• Avoiding catastrophic failure in correlated networks of networks
• Network robustness of multiplex networks with interlayer degree correlations
• Percolation Theory on Interdependent Networks Based on Epidemic Spreading
• Percolation in networks composed of connectivity and dependency links
• Percolation on correlated networks
• Redundant interdependencies boost the robustness of multilayer networks
• Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks
• Weak percolation on multiplex networks
• Competing contagion processes: Complex contagion triggered by simple contagion
• The combined effect of connectivity and dependency links on percolation of networks
• Exotic Critical Behavior of Weak Multiplex Percolation
• Cascading failures in coupled networks with both inner-dependency and inter-dependency links
• Percolation of networks with directed dependency links