On sparsity and power-law properties of graphs based on exchangeable point processes
On sparsity and power-law properties of graphs based on exchangeable point processes
复制标题
基于可交换点过程的图的稀疏性和幂律性质
DOI：
10.1214/12-aap843
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
J. Rousseau
中科院分区：
文献类型：
--
作者：
F. Caron;J. Rousseau
本文研究了基于可交换点过程的图类的性质。我们提供的边缘，节点数和度分布的数量的渐近表达式，确定四个政权：一个密集的政权，稀疏，几乎密集的政权，稀疏政权与幂律的行为，和一个几乎非常稀疏的政权。我们的研究结果使我们能够得到一个一致的估计的标量参数调谐图的稀疏性。我们还提出了一类模型在这个框架内，人们可以分别控制本地，潜在的结构和全局稀疏性/幂律特性的图形。
This paper investigates properties of the class of graphs based on exchangeable point processes. We provide asymptotic expressions for the number of edges, number of nodes and degree distributions, identifying four regimes: a dense regime, a sparse, almost dense regime, a sparse regime with power-law behavior, and an almost extremely sparse regime. Our results allow us to derive a consistent estimator for the scalar parameter tuning the sparsity of the graph. We also propose a class of models within this framework where one can separately control the local, latent structure and the global sparsity/power-law properties of the graph.