Author:
Ozbay Sinan A.,Nguyen Maximilian M.
Abstract
AbstractWe present a simple method to quantitatively capture the heterogeneity in the degree distribution of a network graph using a single parameter $$\sigma$$
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.
Funder
Global Health Program, Princeton University, United States
William H. Miller III Trust
Google
James S. McDonnell Foundation
Publisher
Springer Science and Business Media LLC
Subject
Computational Mathematics,Computer Networks and Communications,Multidisciplinary
Cited by
1 articles.
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