Emergence of coexisting percolating clusters in networks

Area of Science:

• Network science
• Statistical physics
• Complex systems

Background:

• Percolation theory typically assumes only one percolating cluster can exist in a network.
• Limited mixing between network modules can lead to unexpected network behaviors.
• Existing theories like message passing (MP) may be inaccurate for networks with limited interconnections.

Purpose of the Study:

• To challenge the assumption of a single percolating cluster in network theories.
• To introduce a novel approach for modeling multiple coexisting percolating clusters (CPCs).
• To improve the accuracy of percolation predictions in networks with limited mixing.

Main Methods:

• Development of the modular message passing (MMP) approach.
• Verification of MMP through simulations and analysis.
• Comparison of MMP predictions against the message passing (MP) approach.

Main Results:

• Demonstration that several coexisting percolating clusters (CPCs) can emerge in networks with limited mixing.
• Identification of CPCs as a source of inaccuracy in current percolation theories.
• Significant improvement of MMP over MP predictions on synthetic and real-world networks.

Conclusions:

• The existence of CPCs is a critical factor in understanding network percolation.
• The MMP approach provides a more accurate framework for analyzing networks with limited mixing.
• Findings have implications for network robustness and epidemic modeling (e.g., susceptible-infected-recovered - SIR).