Modeling diffusion in networks with communities: A multitype branching process approach

Area of Science:

• Network Science
• Mathematical Modeling
• Epidemiology

Background:

• Diffusion processes in complex networks are crucial for understanding the spread of various entities.
• Existing tools often lack the capacity to analyze diffusion within networks exhibiting community structures.
• Analyzing contagion dynamics in interconnected systems with community structure requires advanced theoretical approaches.

Purpose of the Study:

• To develop theoretical tools for modeling and analyzing diffusion processes in networks with community structure.
• To enable the calculation of key propagation dynamics characteristics using limited network information.
• To estimate the probability of inter-community spread.

Main Methods:

• Utilizing multitype branching processes to model diffusion.
• Employing simple contagion mechanisms for propagation.
• Analyzing network properties based on degree distribution within and between communities.

Main Results:

• Developed a framework to calculate extinction probability, hazard function, and cascade size distribution for entire networks and individual communities.
• Successfully estimated the probability of spread between communities.
• Demonstrated framework accuracy on stochastic block and log-normal networks.
• Showcased the framework's ability to capture the effect of initial seeding location on cascade size distribution in heavy-tailed networks.

Conclusions:

• The developed theoretical framework provides accurate insights into diffusion dynamics in complex, community-structured networks.
• The approach allows for detailed analysis of propagation, including inter-community spread, using minimal network data.
• This work offers valuable tools for understanding and predicting the spread of information, diseases, or behaviors in structured environments.