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: (i) a dense regime, (ii) a sparse almost dense regime, (iii) a sparse regime with power-law behaviour, and (iv) an almost extremely sparse regime. We show that under mild assumptions, both the global and local clustering coefficients converge to constants which may or may not be the same. We also derive a central limit theorem for the number of nodes. Finally, we propose a class of models within this framework where one can separately control the latent structure and the global sparsity/power-law properties of the graph.

翻译：本文根据可交换点进程调查图表类别属性。 我们对边缘数、节点数和度分布提供了无症状的表达方式,确定了四个制度:(一) 密集制度,(二) 稀少的几乎密集的制度,(三) 权力法行为的稀疏制度,(四) 几乎极为稀少的制度。我们显示,在温和假设下,全球和当地组群系数都汇合到可能相同或不同的常数。我们还为节点数得出了一个核心限值。最后,我们在此框架内提出了一组模型,可以分别控制图的潜在结构和全球宽度/功率法特性。