论文标题
$ d+1 $尺寸的随机双曲图
Random hyperbolic graphs in $d+1$ dimensions
论文作者
论文摘要
我们考虑在任何维度$ d+1 \ geq 2 $的双曲线空间中随机双曲线图。我们提出了模型参数的重新缩放，该模型参数将任何维度的随机双曲图模型投入到统一的数学框架上，从而使程度分布相对于维度不变。与学位分布不同，聚类的确取决于尺寸，在$ d \ rightarrow \ infty $下降至0。我们分析了模型的所有其他限制机制，并发布了一个软件包，该软件包在任何维度的双曲线空间中生成随机双曲线图及其限制。
We consider random hyperbolic graphs in hyperbolic spaces of any dimension $d+1\geq 2$. We present a rescaling of model parameters that casts the random hyperbolic graph model of any dimension to a unified mathematical framework, leaving the degree distribution invariant with respect to the dimension. Unlike the degree distribution, clustering does depend on the dimension, decreasing to 0 at $d \rightarrow \infty$. We analyze all of the other limiting regimes of the model, and we release a software package that generates random hyperbolic graphs and their limits in hyperbolic spaces of any dimension.
