Parameterizing network graph heterogeneity using a modified Weibull distribution

We present a simple method to quantitatively capture the heterogeneity in the degree distribution of a network graph using a single parameter σ . Using an exponential transformation of the shape parameter of the Weibull distribution, this control parameter allows the degree distribution to be easily...

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Bibliographic Details
Published inApplied network science Vol. 8; no. 1; p. 20
Main Authors Ozbay, Sinan A., Nguyen, Maximilian M.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2023
Springer Nature B.V
SpringerOpen
Subjects
Algorithms
Complexity
Computer Appl. in Social and Behavioral Sciences
Computer Science
Graphs
Heterogeneity
Parameterization
Parameters
Simulation and Modeling
Spectrum analysis
Weibull distribution
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Summary:We present a simple method to quantitatively capture the heterogeneity in the degree distribution of a network graph using a single parameter σ . Using an exponential transformation of the shape parameter of the Weibull distribution, this control parameter allows the degree distribution to be easily interpolated between highly symmetric and highly heterogeneous distributions on the unit interval. This parameterization of heterogeneity also recovers several other canonical distributions as intermediate special cases, including the Gaussian, Rayleigh, and exponential distributions. We then outline a general graph generation algorithm to produce graphs with a desired amount of heterogeneity. The utility of this formulation of a heterogeneity parameter is demonstrated with examples relating to epidemiological modeling and spectral analysis.
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ISSN:2364-8228
2364-8228
DOI:10.1007/s41109-023-00544-9