Higher-order structure and epidemic dynamics in clustered networks.

Area of Science:

• Network science
• Computational epidemiology
• Complex systems

Background:

• Traditional network analysis often focuses on clustering coefficients (triangle ratios).
• Existing models for network generation and dynamics are limited for complex, overlapping structures.
• Higher-order structures beyond simple triangles are not well-quantified.

Purpose of the Study:

• To demonstrate that networks with same degree distribution and clustering can have different higher-order structures.
• To develop a novel network metric for quantifying order-four structures.
• To investigate the impact of higher-order network topology on epidemic dynamics.

Main Methods:

• Generated homogeneous networks with equal clustering using a modified configuration model and rewiring algorithms.
• Developed and applied a new metric to measure order-four network structures.
• Simulated Susceptible-Infected-Susceptible (SIS) and Susceptible-Infected-Recovered (SIR) epidemic models on generated networks.

Main Results:

• Networks with identical clustering and degree distributions can exhibit distinct higher-order structures (e.g., overlapping triangles).
• The new metric successfully quantifies these order-four structural differences.
• Differences in higher-order structure significantly influenced epidemic thresholds, prevalence, and temporal dynamics.

Conclusions:

• Standard network metrics like clustering are insufficient to capture the full topological complexity.
• Quantifying higher-order network structures is essential for a deeper understanding of network-driven phenomena.
• Network topology, particularly its higher-order features, plays a critical role in modulating epidemic spread.