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Updated: May 11, 2025

3D Modeling of Dendritic Spines with Synaptic Plasticity

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Published on: May 18, 2020

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

Alina Dubovskaya^1,2, Caroline B Pena², David J P O'Sullivan²

¹University of Limerick, Department of Psychology, Centre for Social Issues Research, Limerick V94T9PX, Ireland.

Physical Review. E

|April 18, 2025

Summary

This study introduces a new theoretical framework using multitype branching processes to analyze diffusion dynamics in complex networks with community structures. The model accurately predicts propagation characteristics and spread between communities.

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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.