Topological data analysis of contagion maps for examining spreading processes on networks

Area of Science:

• Network Science
• Epidemiology
• Topological Data Analysis

Background:

• Social and biological contagions are affected by network structures.
• Modern contagions can spread globally via long-range connections, unlike historical wave-like epidemics.
• Understanding these spread dynamics is crucial for public health and network analysis.

Purpose of the Study:

• To develop a new methodology for studying contagion spread on networks.
• To utilize topological data analysis and nonlinear dimension reduction for network analysis.
• To create 'contagion maps' for visualizing and analyzing spreading processes.

Main Methods:

• Constructing 'contagion maps' by mapping network nodes as point clouds based on multiple contagions.
• Applying topological data analysis to study the geometry and dimensionality of the resulting point clouds.
• Utilizing nonlinear dimension reduction techniques to analyze manifold structures.

Main Results:

• Revealed insights into the modeling, forecasting, and control of spreading processes.
• Demonstrated the effectiveness of contagion maps in analyzing complex network dynamics.
• Showcased contagion maps as a tool for inferring low-dimensional network structures.

Conclusions:

• Contagion maps offer a powerful new approach to understanding contagion spread.
• The methodology aids in predicting and controlling epidemics in complex networks.
• This technique can also be used to uncover underlying low-dimensional structures within networks.