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Published on: December 18, 2016
Spectral analysis of deformed random networks.
1Max-Planck Institute for the Physics of Complex Systems, Dresden, Germany. physarik@nus.edu.sg
Introducing connections into random networks with community structure shifts spectral behavior. This transition, from Poisson to Gaussian orthogonal ensemble statistics, reveals network deformation insights, applicable to protein-protein interaction networks.
Area of Science:
- Network science
- Random matrix theory
- Statistical physics
Background:
- Sparsely connected random networks exhibit community structures.
- Random matrix theory provides a framework for analyzing spectral properties.
- Network deformation can alter spectral statistics.
Purpose of the Study:
- To investigate the spectral behavior of random networks with evolving community structures.
- To analyze the transition of spectral statistics from Poisson to Gaussian orthogonal ensemble (GOE).
- To assess the utility of spectral rigidity and spacing distributions in characterizing network deformation.
Main Methods:
- Applying the random matrix framework to analyze network spectra.
- Introducing connections between subnetworks to model deformation.
- Calculating eigenvalue density, spacing distributions, and Dyson-Mehta Delta3 statistics.
- Analyzing a real-world protein-protein interaction network.
Main Results:
- Introducing inter-subnetwork connections induces a spectral transition from Poisson to GOE statistics.
- Eigenvalue density transitions to Wigner's semicircular behavior with increasing deformation.
- Spectral rigidity's GOE regime depends on deformation strength.
- Spacing distribution detects slight deformations, while Delta3 statistics are sensitive to larger ones.
Conclusions:
- Spectral statistics serve as sensitive indicators of network deformation from perfect community structures.
- Different spectral measures (spacing, density, Delta3) capture varying degrees of deformation.
- The findings are validated by analyzing a Helicobacter protein-protein interaction network spectrum.
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