Network Higher-Order Structure Dismantling.

Area of Science:

• Network Science
• Complex Systems Analysis
• Graph Theory

Background:

• Higher-order structures are crucial for network meta-functions, functionality, and complex dynamics.
• Dismantling these structures to achieve functional paralysis has been largely overlooked.
• The diversity and unknown specifics of higher-order structures make individual targeting infeasible.

Purpose of the Study:

• Introduce the concept of dismantling higher-order structures for complete network functional paralysis.
• Develop a method to disrupt both network connectivity and all higher-order structures.
• Address the challenge of targeting diverse and unspecified higher-order structures.

Main Methods:

• Leverage the association between higher-order structures and k-cores due to high internal connectivity.
• Transform higher-order structure measurement into k-core measurements.
• Propose the Belief Propagation-guided Higher-order Dismantling (BPHD) algorithm to minimize costs and maximize disruption.

Main Results:

• The BPHD algorithm effectively dismantles higher-order structures, converting networks into forests.
• Demonstrated the explosive vulnerability of network higher-order structures.
• Observed counterintuitive decreasing dismantling costs with increasing structural complexity.

Conclusions:

• The BPHD algorithm provides a novel approach for dismantling malignant networks.
• Safeguarding against malicious attacks targeting higher-order structures presents substantial challenges.
• This work highlights the critical need to understand and defend against higher-order structure manipulation.