Message passing theory for percolation models on multiplex networks with link overlap.

Area of Science:

• Complex Systems Science
• Network Science
• Statistical Physics

Background:

• Multiplex networks, common in infrastructure and biology, often exhibit significant link overlap.
• Characterizing the mutually connected giant component is crucial for understanding these systems.
• Existing models often do not account for link overlap in multilayered networks.

Purpose of the Study:

• To develop a message passing theory for percolation transitions in multiplex networks with link overlap.
• To propose and compare two novel message passing algorithms for analyzing these networks.
• To characterize the emergence of the mutually connected giant component and directed percolation.

Main Methods:

• Developed a generalized message passing theory for multiplex networks with arbitrary layers (M) and link overlap.
• Proposed two message passing algorithms: one for directed percolation (epidemic spreading interpretation) and one for giant component emergence.
• Analyzed phase diagrams for percolation and directed percolation in representative network structures.

Main Results:

• The proposed algorithms generalize existing methods for networks without link overlap.
• Directed percolation exhibits nontrivial tricritical points in certain multiplex network structures.
• Percolation transition for the giant component is discontinuous, except in cases of complete layer overlap.

Conclusions:

• The message passing theory effectively characterizes percolation transitions in multiplex networks with link overlap.
• The distinction between directed percolation and giant component emergence is critical for understanding network behavior.
• Findings provide insights into the resilience and dynamics of complex multilayered systems.