Dynamic topology and percolation criticality in higher-order activity-vulnerability driven networks

Area of Science:

• Network Science
• Complex Systems Dynamics
• Computational Social Science

Background:

• Temporal higher-order networks are vital for predicting phenomena like information spread and systemic resilience.
• Existing models, such as the higher-order activity-driven framework, primarily focus on connection formation, neglecting node dissolution, which can bias predictions of network evolution and stability.

Purpose of the Study:

• To introduce a novel framework, higher-order activity-vulnerability driven (HOAVD) networks, that simultaneously models hyperedge formation and dissolution.
• To analyze the dynamic phase transition induced by the interplay of node activity and vulnerability.
• To derive analytical expressions for network topological properties and identify critical conditions for system-wide percolation.

Main Methods:

• Development of the HOAVD network model incorporating node activity and vulnerability for hyperedge dynamics.
• Analytical derivation of network topological properties and percolation conditions.
• Numerical simulations using real-world data to validate analytical findings.

Main Results:

• The HOAVD framework demonstrates a gradual dynamic phase transition at a characteristic timescale, separating dynamics into activity-dominated and balanced regimes.
• Analytical expressions for topological properties and a critical balance condition for percolation in the balanced regime were derived.
• The critical balance condition highlights the sensitive dependence of connectivity on the interplay between activity and vulnerability distributions, a mechanism previously overlooked.

Conclusions:

• The HOAVD network framework provides a more comprehensive and physically grounded approach to understanding temporal higher-order network dynamics.
• The findings offer crucial insights into time-dependent network topology and the fundamental mechanisms governing network evolution.
• This framework enhances the ability to predict and control dynamics in diverse systems, including social, biological, and technological networks.