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Published on: December 18, 2016
Approximating spectral impact of structural perturbations in large networks
Attilio Milanese1, Jie Sun, Takashi Nishikawa
1Department of Mechanical & Aeronautical Engineering, Clarkson University, Potsdam, New York 13699-5725, USA. amilanes@cern.ch
Summary
This study introduces a theory to estimate how network changes affect eigenvalue spectra, crucial for understanding network dynamics. The findings enable accurate subgraph ranking in complex networks.
Area of Science:
- Network science
- Graph theory
- Applied mathematics
Background:
- Eigenvalue spectra of networks reveal topological structure and dynamical behaviors like synchronization.
- Understanding how structural changes impact these spectra is vital for network analysis.
Purpose of the Study:
- To develop a theory for estimating eigenvalue spectral changes in networks due to link additions or removals.
- To provide methods for ranking subgraphs within complex networks based on spectral properties.
Main Methods:
- Developing approximation schemes for the largest eigenvalue of the adjacency matrix and extreme eigenvalues of the graph Laplacian.
- Applying these schemes to real and artificial networks.
- Proposing a local iterative scheme using neighbor connectivity information.
Main Results:
- Demonstrated effectiveness of approximation schemes in estimating spectral changes.
- Accurate spectral ranking of small subgraphs was achieved.
- A local iterative scheme was proposed for efficient subgraph ranking.
Conclusions:
- The developed theory accurately estimates spectral changes in networks following structural perturbations.
- The methods offer practical applications for ranking subgraphs in real-world complex networks.
- Results enhance theoretical understanding of network dynamics and subgraph importance.
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