This paper investigates the distributions of triangle counts per vertex and edge, as a means for network description, analysis, model building, and other tasks. The main interest is in estimating these distributions through sampling, especially for large networks. A novel sampling method tailored for the estimation analysis is proposed, with three sampling designs motivated by several network access scenarios. An estimation method based on inversion and an asymptotic method are developed to recover the entire distribution. A single method to estimate the distribution using multiple samples is also considered. Algorithms are presented to sample the network under the various access scenarios. Finally, the estimation methods on synthetic and real-world networks are evaluated in a data study.

中文翻译：

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大型网络中三角形计数分布的采样方法和估计

本文研究了每个顶点和边的三角形计数分布，作为网络描述、分析、模型构建和其他任务的一种手段。主要兴趣在于通过抽样估计这些分布，特别是对于大型网络。提出了一种为估计分析量身定制的新采样方法，其中三种采样设计受多个网络访问场景的启发。开发了一种基于反演和渐近方法的估计方法来恢复整个分布。还考虑了使用多个样本估计分布的单一方法。提出了在各种接入场景下对网络进行采样的算法。最后，在数据研究中评估了合成网络和真实网络的估计方法。