Percolation transitions are not always sharpened by making networks interdependent

Area of Science:

• Network Science
• Statistical Physics
• Complex Systems

Background:

• Coupled network models require nodes to connect via two link types for viability.
• Previous research suggested coupled networks exhibit more abrupt percolation transitions than uncoupled networks, often found to be discontinuous.
• The nature of percolation transitions in coupled networks requires further investigation across different network structures.

Purpose of the Study:

• To analyze the percolation transition in coupled network models.
• To verify and extend findings on the abruptness of transitions in coupled Erdös-Rényi networks.
• To investigate the transition behavior in fully interdependent diluted lattices.

Main Methods:

• Utilized an efficient new algorithm for analyzing network percolation.
• Simulated node removal in coupled Erdös-Rényi networks and diluted lattices.
• Calculated the order parameter exponent (β) in 2 and 3 dimensions.

Main Results:

• Confirmed discontinuous percolation transitions for coupled Erdös-Rényi networks.
• Discovered continuous percolation transitions for fully interdependent diluted lattices.
• Observed a larger order parameter exponent (β) in 2D and 3D diluted lattices compared to ordinary percolation, indicating less sharp transitions.

Conclusions:

• The abruptness of percolation transitions in coupled networks is dependent on the network's specific structure.
• Fully interdependent diluted lattices exhibit continuous transitions, contrasting with previous claims for coupled systems.
• Findings suggest that spatially embedded networks may display transition behaviors further from discontinuity than isolated networks.