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Related Experiment Video

Updated: May 15, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

Robustness of random graphs based on graph spectra.

Jun Wu1, Mauricio Barahona, Yue-Jin Tan

  • 1College of Information Systems and Management, National University of Defense Technology, Changsha 410073, People's Republic of China. wujunpla@hotmail.com

Chaos (Woodbury, N.Y.)
|January 3, 2013
PubMed
Summary
This summary is machine-generated.

Natural connectivity, a network robustness measure, increases linearly with average degree in Erdős-Rényi graphs. These graphs are more robust than random regular graphs but less robust than ring lattices above a critical size.

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Last Updated: May 15, 2026

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
07:11

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

Published on: August 19, 2021

Area of Science:

  • Network science
  • Graph theory
  • Spectral graph theory

Background:

  • Complex network robustness is crucial for system reliability.
  • Natural connectivity, an average Estrada index, offers a spectral method to assess network robustness.
  • This index relates to graph eigenvalues and Helmholtz free energy.

Purpose of the Study:

  • To evaluate the natural connectivity index for characterizing the robustness of different network models.
  • To compare the robustness of Erdős-Rényi (ER) random graphs, random regular graphs, and regular ring lattices using natural connectivity.

Main Methods:

  • Analytical derivations of natural connectivity for various graph types.
  • Numerical simulations to validate analytical findings.
  • Comparative analysis of robustness based on natural connectivity values.

Main Results:

  • Natural connectivity of ER random graphs scales linearly with the average degree.
  • ER random graphs demonstrate greater robustness than random regular graphs with similar parameters.
  • The relative robustness of ER graphs versus ring lattices is size- and degree-dependent, with a critical size identified.

Conclusions:

  • Natural connectivity effectively characterizes the robustness of ER random graphs, random regular graphs, and ring lattices.
  • Analytical framework derived to determine the critical graph size for robustness comparison between ER graphs and ring lattices.