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Epidemic threshold in directed networks.

Cong Li¹, Huijuan Wang¹, Piet Van Mieghem¹

¹Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Delft, The Netherlands.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 4, 2014

Summary

This summary is machine-generated.

Directed networks, unlike undirected ones, better model real-world spread of information. Increasing directionality in networks lowers the epidemic threshold, making spread slower and random walks converge faster.

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Area of Science:

Network Science
Epidemiology
Complex Systems

Background:

Epidemics are typically studied in undirected networks, which do not fully represent real-world systems like social media or the web.
Many real-world networks are directed, featuring unidirectional and bidirectional links, influencing the spread of information, emotions, or malware.

Purpose of the Study:

To investigate the impact of network directionality on epidemic spread and network properties.
To develop algorithms for generating directed networks with specific directionality parameters.

Main Methods:

Defined directionality (ξ) as the percentage of unidirectional links in a network.
Proposed two algorithms to generate directed networks with a specified directionality.
Analyzed the effect of directionality on spectral radius (λ(1)), principal eigenvector (x(1)), spectral gap, and algebraic connectivity.

Main Results:

Spectral radius (λ(1)) decreases as directionality (ξ) increases.
Spectral gap and algebraic connectivity increase with directionality (ξ).
The decrease in spectral radius is influenced by degree distribution and degree-degree correlation.

Conclusions:

Directed networks exhibit a larger epidemic threshold compared to undirected networks with similar degree distributions.
Random walks on directed networks converge to their steady state faster than on undirected networks.