论文标题
使用修改的Weibull分布的参数化网络图异质性
Parameterizing Network Graph Heterogeneity using a Modified Weibull Distribution
论文作者
论文摘要
我们提出了一种简单的方法，可以使用单个参数$σ$定量地捕获网络图的度分布中的异质性。使用Weibull分布的形状参数的指数转换，此控制参数允许在单位间隔上轻松地在高度对称和高度异构分布之间插值度分布。异质性的这种参数化还恢复了其他几个规范分布，例如中间特殊情况，包括高斯，瑞利和指数分布。然后，我们概述了一般图生成算法，以产生具有所需数量异质性的图形。与流行病学建模和光谱分析有关的示例证明了这种异质性参数的表述的实用性。
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.
