Percolation and epidemic thresholds in clustered networks

Area of Science:

• Network Science
• Statistical Physics
• Complex Systems

Background:

• Scale-free networks exhibit unique properties due to their heterogeneous degree distributions.
• Clustering, or the tendency of nodes to form tightly connected groups, is prevalent in many real-world networks.
• Percolation theory studies the formation of connected components in random networks.

Purpose of the Study:

• To theoretically investigate the impact of clustering on percolation in scale-free networks.
• To determine if clustering can induce a finite percolation threshold in these networks.
• To assess the implications for epidemic thresholds in clustered scale-free networks.

Main Methods:

• Development of a theoretical framework for analyzing percolation in clustered random networks.
• Mathematical analysis of percolation properties, including the giant connected component.
• Comparison of theoretical predictions with numerical simulations.

Main Results:

• Clustering significantly influences percolation properties like component size and resilience.
• Clustering does not re-establish a finite percolation threshold in scale-free networks.
• The absence of a percolation threshold implies no epidemic threshold in these networks.

Conclusions:

• The theoretical approach provides insights into percolation dynamics in clustered scale-free networks.
• The findings extend to a broad range of real-world networks with high transitivity.
• The absence of an epidemic threshold is a key consequence for understanding network resilience and spread phenomena.