We introduce a new methodology for model selection in the context of modeling network data. The statistical network analysis literature has developed many different classes of network data models, with notable model classes including stochastic block models, latent position models, and exponential families of random graph models. A persistent question in the statistical network analysis literature lies in understanding how to compare different models for the purpose of model selection and evaluating goodness-of-fit, especially when models have different mathematical foundations. In this work, we develop a novel non-parametric method for model selection in network data settings which exploits the information contained in the spectrum of the graph Laplacian in order to obtain a measure of goodness-of-fit for a defined set of network data models. We explore the performance of our proposed methodology to popular classes of network data models through numerous simulation studies, demonstrating the practical utility of our method through two applications.

翻译：统计网络分析文献已发展了网络数据模型的许多不同类别,有显著的模型类别,包括随机图形模型的整块模型、潜在位置模型和指数型图解模型。统计网络分析文献中持续存在的一个问题是如何了解如何为模型选择和评估良好条件而比较不同的模型,特别是当模型具有不同的数学基础时。在这项工作中,我们开发了一种新的非参数方法,用于网络数据设置中的模型选择,利用Laplacian图光谱所含的信息,以便获得一套界定的网络数据模型的适宜度。我们通过许多模拟研究,探索我们为广受欢迎的网络数据模型拟议方法的绩效,通过两种应用展示我们方法的实际效用。