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Parameterizing network graph heterogeneity using a modified Weibull distribution.

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  • 1Bendheim Center for Finance, Princeton University, Princeton, NJ USA.

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This summary is machine-generated.

We introduce a new parameter to quantify network graph heterogeneity. This single parameter interpolates between symmetric and heterogeneous degree distributions, simplifying network analysis and generation.

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Area of Science:

  • Network Science
  • Graph Theory
  • Statistical Modeling

Background:

  • Understanding network heterogeneity is crucial for analyzing complex systems.
  • Existing methods for quantifying degree distribution heterogeneity can be complex.
  • A unified parameter is needed to describe the spectrum of network structures.

Purpose of the Study:

  • To develop a single, quantitative parameter to capture network graph heterogeneity.
  • To enable interpolation between different types of degree distributions.
  • To provide a general algorithm for generating graphs with controlled heterogeneity.

Main Methods:

  • Utilizing an exponential transformation of the Weibull distribution's shape parameter.
  • Developing a control parameter ranging from 0 to 1 for heterogeneity.
  • Outlining a general graph generation algorithm based on the heterogeneity parameter.

Main Results:

  • A single parameter effectively quantifies heterogeneity in degree distributions.
  • The parameter allows interpolation between symmetric (e.g., Gaussian) and heterogeneous (e.g., exponential) distributions.
  • Canonical distributions like Gaussian, Rayleigh, and exponential are recovered as special cases.

Conclusions:

  • The proposed parameter offers a simple yet powerful way to characterize network heterogeneity.
  • This formulation facilitates the generation of synthetic networks with tunable properties.
  • Applications in epidemiological modeling and spectral analysis demonstrate the parameter's utility.