A simple model of global cascades on random networks

Area of Science:

• Network Science
• Complex Systems
• Sociophysics

Background:

• Large cascades, from cultural trends to infrastructure failures, originate from minor initial shocks.
• Understanding the mechanisms behind these rare, large-scale events is crucial across diverse fields.

Purpose of the Study:

• To explain the origin of large, rare cascades in networks of interacting agents.
• To identify network conditions that lead to global cascades and analyze their predictability.

Main Methods:

• Modeling a sparse, random network of agents with decisions based on neighbors' actions and a threshold rule.
• Analyzing two distinct network regimes based on connectivity and node stability.

Main Results:

• Identified two regimes susceptible to rare global cascades.
• Observed power law distribution of cascade sizes in less connected networks, and bimodal distribution in highly connected networks.
• Found that highly connected nodes are more likely to trigger cascades in skewed networks, but not in highly connected ones.

Conclusions:

• Network connectivity and local node stability critically influence cascade size distribution and predictability.
• Heterogeneity in thresholds increases vulnerability, while heterogeneity in degree distribution enhances stability.