Scaling properties of scale-free networks in degree-thresholding renormalization flows

Abstract

We study the statistical properties of observables of scale-free networks in the degree-thresholding renormalization (DTR) flows. For BA scale-free networks with different sizes, we find that their structural and dynamical observables have similar scaling behavior in the DTR flow. The finite-size scaling analysis confirms this view and reveals a scaling function with a single scaling exponent that collectively captures the changes of these observables. Furthermore, for the scale-free network with a single initial size, we use its DTR snapshots as the original networks in the DTR flows, then perform a similar finite-size scaling analysis. Interestingly, the initial network and its snapshots share the same scaling exponent as the BA synthetic network. Our findings have important guiding significance for analyzing the structure and dynamic behavior of large-scale networks. Such as, in large-scale simulation scenarios with high time complexity, the DTR snapshot could serve as a substitute or guide for the initial network and then quickly explore the scaling behavior of initial networks.

References in corpus (22)

• Emergence of scaling in random networks
• Power-law distributions in empirical data
• Error and attack tolerance of complex networks
• Epidemic spreading in scale-free networks
• Synchronization in small-world systems
• Self-similarity of complex networks
• Powerlaw: a Python package for analysis of heavy-tailed distributions
• Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
• Entangled networks, synchronization, and optimal network topology
• Growing Scale-Free Networks with Small World Behavior
• Self-similarity of complex networks and hidden metric spaces
• The onset of synchronization in large networks of coupled oscillators
• Network Geometry
• Low-temperature behavior of two-dimensional Gaussian Ising spin glasses
• Multiscale unfolding of real networks by geometric renormalization
• True scale-free networks hidden by finite size effects
• Complex networks renormalization: flows and fixed points
• Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects
• Detecting the ultra low dimensionality of real networks
• Renormalization flows in complex networks
• Sensitive Dependence of Optimal Network Dynamics on Network Structure
• Finite-size scaling of geometric renormalization flows in complex networks