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Predicting percolation thresholds in networks.

Filippo Radicchi1

  • 1Center for Complex Networks and Systems Research, School of Informatics and Computing, Indiana University, Bloomington, Indiana 47405, USA.

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Summary
This summary is machine-generated.

Predicting network percolation thresholds without simulations is challenging. While graph eigenvalues offer a lower bound, simple degree distribution moments are often more accurate, especially for fragile networks.

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Area of Science:

  • Network science
  • Statistical physics
  • Graph theory

Background:

  • Percolation thresholds are critical for understanding network robustness.
  • Predicting these thresholds often relies on computationally intensive simulations.
  • Developing analytical methods for threshold approximation is essential.

Purpose of the Study:

  • To evaluate non-simulation-based methods for approximating percolation thresholds in networks.
  • To assess the effectiveness and reliability of these prediction tools on synthetic and real-world networks.
  • To identify robust indicators for network percolation behavior.

Main Methods:

  • Analysis of synthetic graphs and 109 real-world networks.
  • Evaluation of the inverse largest eigenvalue of the nonbacktracking matrix as a predictor.
  • Comparison with expectation values based on degree distribution moments.
  • Systematic quantification of prediction accuracy and reliability.

Main Results:

  • The inverse largest eigenvalue of the nonbacktracking matrix often provides a tight lower bound for the percolation threshold.
  • In over 40% of cases, degree distribution moments were more predictive than the eigenvalue method.
  • The predictive performance of all tested indicators degrades as the true percolation threshold increases.
  • No single indicator reliably predicts the robustness of highly fragile networks.

Conclusions:

  • Current analytical methods, including graph eigenvalues, have limitations in accurately predicting percolation thresholds, especially for fragile networks.
  • Degree distribution moments can be surprisingly effective, outperforming more complex graph-theoretic measures in certain scenarios.
  • Further research is needed to develop reliable proxies for network robustness, particularly for networks with low thresholds.