Message-passing approach for threshold models of behavior in networks

Area of Science:

• Social network analysis
• Computational sociology
• Mathematical modeling of social dynamics

Background:

• Social behaviors, such as trends and opinions, spread through networks.
• Individual adoption of behaviors is often influenced by the number of neighbors already exhibiting the behavior, defined by a threshold (T).
• Existing models may lack computational efficiency or complete time evolution tracking.

Purpose of the Study:

• To develop a computationally efficient method for modeling social behavior propagation in networks.
• To provide a complete time evolution of adoption probabilities for individuals.
• To offer a generalizable framework for complex agent-based models.

Main Methods:

• A dynamic message-passing algorithm was developed.
• The method tracks the probability of each individual adopting a trend over time.
• Validation was performed using Monte Carlo simulations and analytic schemes for large random networks.

Main Results:

• The developed method provides a tractable and computationally efficient way to simulate behavior propagation.
• The method accurately predicts the time evolution of adoption frequencies in various network structures.
• Exact analytic results were derived for large random networks, showing good agreement with simulations.

Conclusions:

• The dynamic message-passing algorithm offers a powerful tool for understanding social contagion.
• The approach is versatile, accommodating non-Markovian processes and heterogeneous thresholds.
• This framework enables the exploration of complex heterogeneous agent-based models in social science research.