Abstract

A variety of random graph models have been proposed in the literature to model the associations within an interconnected system and to realistically account for various structures and attributes of such systems. In particular, much research has been devoted to modeling the interaction of humans within social networks. However, such networks in real-life tend to be extremely sparse and existing methods do not adequately address this issue. In this article, we propose an extension to ordinary and degree corrected stochastic blockmodels that accounts for a high degree of sparsity. Specifically, we propose hurdle versions of these blockmodels to account for community structure and degree heterogeneity in sparse networks. We use simulation to ensure parameter estimation is consistent and precise, and we propose the use of likelihood ratio-type tests for model selection. We illustrate the necessity for hurdle blockmodels with a small research collaboration network as well as the infamous Enron E-mail exchange network. Methods for determining goodness of fit and performing model selection are also proposed. Supplementary materials for this article are available online.

摘要

文献中提出了各种随机图模型来对互连系统内的关联进行建模，并实际说明此类系统的各种结构和属性。特别是，很多研究都致力于对社交网络中的人类交互进行建模。然而，现实生活中的此类网络往往非常稀疏，现有方法无法充分解决这个问题。在本文中，我们提出了对普通和程度校正随机块模型的扩展，该模型考虑了高度的稀疏性。具体来说，我们提出了这些块模型的障碍版本，以解释稀疏网络中的社区结构和程度异质性。我们使用模拟来确保参数估计的一致性和精确性，我们建议使用似然比类型测试进行模型选择。我们用一个小型研究协作网络以及臭名昭著的安然电子邮件交换网络来说明障碍块模型的必要性。还提出了确定拟合优度和执行模型选择的方法。本文的补充材料可在线获取。