Enhanced robustness of single-layer networks with redundant dependencies

Area of Science:

• Network Science
• Statistical Physics
• Complex Systems

Background:

• Dependency links model nonlocal effects in networked systems.
• The weak dependency model relaxes rules, allowing nodes to function if at least one dependency neighbor is active.

Purpose of the Study:

• Investigate percolation properties in networks with weak dependency links.
• Analyze critical phenomena and network robustness in Erdős-Rényi and scale-free networks.

Main Methods:

• Studied percolation in Erdős-Rényi and random scale-free networks with dependency links.
• Analyzed continuous and discontinuous percolation transitions and identified critical points.

Main Results:

• Identified a stability "cusp" point irrespective of dependency link density.
• Observed hybrid percolation transitions and a tricritical point in Erdős-Rényi networks.
• Found critical points and double transitions in scale-free networks, with a unique singularity S-S_{c}∝(p-p_{c})^{1/4}.

Conclusions:

• Weak dependency models lead to more robust structures and diverse critical phenomena.
• Scale-free networks exhibit high resilience, particularly with correlated dependency degrees and protected hubs.