  We present a simple method to quantitatively capture the heterogeneity in the
degree distribution of a network graph using a single parameter $\sigma$. 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.
