Reconstruction of evolved dynamic networks from degree correlations
Steffen Karalus1, Joachim Krug1
1Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, D-50937 Köln, Germany.
Physical Review. E
|July 15, 2016
Summary
Network structure significantly impacts spectral properties. Two-point degree correlations are crucial for achieving power-law scaling in network Laplacian spectra, more so than degree distribution or clustering alone.
Area of Science:
- Network Science
- Complex Systems
- Spectral Graph Theory
Background:
- Networks often exhibit power-law scaling in their Laplacian spectrum, a property linked to their structural characteristics.
- Understanding which local structural properties drive this spectral scaling is essential for network analysis and design.
Purpose of the Study:
- To investigate the influence of local network structural properties on power-law scaling in the Laplacian spectrum.
- To determine the relative importance of degree distribution, two-point degree correlations, and degree-dependent clustering in generating spectral scaling.
Main Methods:
- Evolving networks to achieve power-law scaling in the Laplacian spectrum.
- Extracting local structural properties: degree distribution, two-point degree correlations, and degree-dependent clustering.
- Constructing random networks with prescribed distributions to isolate the effects of each property.
Main Results:
- Degree distribution alone is insufficient to replicate the observed spectral scaling.
- Degree-dependent clustering shows only an indirect influence on the spectral scaling.
- Two-point degree correlations emerge as the dominant characteristic for achieving power-law spectral scaling over a wide eigenvalue range.
Conclusions:
- Local structural properties play a critical role in determining the spectral characteristics of evolved networks.
- Two-point degree correlations are the key feature responsible for the power-law scaling in Laplacian spectra.
- Future network models aiming for specific spectral properties should prioritize the accurate representation of two-point degree correlations.
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