Response to targeted perturbations for random walks on networks

Area of Science:

• Network Science
• Statistical Physics
• Complex Systems

Background:

• Understanding transport dynamics on networks is crucial for various applications.
• Mean first-passage time (MFPT) is a key metric for evaluating network efficiency.
• Local network perturbations can significantly alter global transport properties.

Purpose of the Study:

• To introduce a general framework for quantifying the impact of local network perturbations on the mean first-passage time (MFPT) to a target node.
• To analyze how network size, perturbation localization, and perturbation intensity affect transport properties.
• To investigate the resilience of transport efficiency to targeted link damage or enhancement.

Main Methods:

• Development of a general analytical framework for random walks on networks.
• Quantification of the response of MFPT to local link additions (enhancement) or removals (attacks).
• Explicit determination of the dependence of MFPT response on network geometry and perturbation intensity.

Main Results:

• The relative variation in MFPT due to local perturbations is independent of network size and remains significant in the large size limit.
• A targeted perturbation has a substantial impact on transport properties, irrespective of the damaged link's localization, especially for non-compact network exploration.
• The framework explicitly determines the relationship between transport response and geometric parameters.

Conclusions:

• Local network perturbations have a profound and size-independent effect on mean first-passage times.
• Network transport properties are sensitive to targeted link modifications, highlighting vulnerabilities and potential optimization strategies.
• The developed framework provides a powerful tool for analyzing and predicting the impact of network changes on diffusion and transport processes.