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Fluctuations in percolation of sparse complex networks.

Ginestra Bianconi¹

¹School of Mathematical Sciences, Queen Mary University of London, London, E1 4NS, United Kingdom.

Physical Review. E

|January 20, 2018

Summary

Fluctuations significantly impact sparse complex network percolation. This study introduces a framework to predict these fluctuations, crucial for understanding network resilience to damage.

Area of Science:

Network science
Statistical physics

Background:

Percolation theory describes how network connectivity changes under node or edge removal.
Understanding fluctuations is key to predicting the behavior of real-world complex networks.

Purpose of the Study:

To investigate the role of fluctuations in the percolation of sparse complex networks.
To develop a predictive framework for network response to damage.

Main Methods:

Considering two random correlated realizations of initial node damage.
Employing a message-passing algorithm for single-network fluctuation prediction.
Developing an analytic prediction for expected fluctuations in network ensembles.

Main Results:

The study quantifies the fraction of nodes remaining in the giant component under different damage scenarios.

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The framework successfully predicts fluctuations in sparse complex networks.

The approach is validated on real ecological and infrastructure networks.

Conclusions:

Fluctuations play a critical role in the percolation dynamics of sparse complex networks.
The developed framework accurately characterizes expected fluctuations in network response to external damage.
This work provides valuable insights for network resilience and robustness analysis.