Scale-free networks well done

2018/11/30 by Ivan Voitalov, Pim van der Hoorn, Remco van der Hofstad +1 · 159 citations
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Complex Network Analysis Techniques #Complex Systems and Time Series Analysis #Key (lock) #Measure (data warehouse) #Power (physics) #Probability distribution #Set (abstract data type) #Statistical Mechanics and Entropy #Statistical model #cs.SI #physics.data-an #physics.soc-ph

paper · pdf · doi:10.1103/physrevresearch.1.033034

published in Physical Review Research 1(3) (American Physical Society)

openalex created_date 2018/11/16 · openalex publication_date 2019/10/18 · arxiv created 2019/10/22 · arxiv updated 2019/10/23 · openalex updated_date 2026/08/06

Abstract

The authors set to propose a rigorous definition of power laws in real-world networks as distributions that are regularly varying. They then explore the statistical significance of this definition in state-of-the-art results.

Citations

• Hyperbolic geometry of complex networks
• Organization of growing random networks
• A Brief History of Generative Models for Power Law and Lognormal Distributions
• Power-Law Distributions in Empirical Data
• Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence
• Heavy tail modeling and teletraffic data: special invited paper
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• Cut-offs and finite size effects in scale-free networks
• Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation
• The random walk's guide to anomalous diffusion: a fractional dynamics approach
• How likely is an i.i.d. degree sequence to be graphical?
• Critical Truths About Power Laws
• Limiting forms of the frequency distribution of the largest or smallest member of a sample
• Ising Critical Exponents on Random Trees and Graphs
• Parameter estimation for power-law distributions by maximum likelihood methods
• The ASA Statement on p -Values: Context, Process, and Purpose
• Scale-free networks are rare
• Moving to a World Beyond “ p < 0.05”

Cited by

• Firm-level production networks: What do we (really) know?
• Deep learning of contagion dynamics on complex networks
• Link prediction with hyperbolic geometry
• Classes of critical avalanche dynamics in complex networks

Related

• Beyond the Power Law: Estimation, Goodness-of-Fit, and a Semiparametric Extension in Complex Networks
• Scale-free networks are rare
• Problems with classification, hypothesis testing, and estimator convergence in the analysis of degree distributions in networks
• The Truth about Power Laws: Theory and Reality
• Extremum statistics in scale-free network models