This article presents a simple and easily implementable Bayesian approach to model and quantify uncertainty in small descriptive social networks. While statistical methods for analyzing networks have seen burgeoning activity over the last decade or so, ranging from social sciences to genetics, such methods usually involve sophisticated stochastic models whose estimation requires substantial structure and information in the networks. At the other end of the analytic spectrum, there are purely descriptive methods based upon quantities and axioms in computational graph theory. In social networks, popular descriptive measures include, but are not limited to, the so called Krackhardt's axioms. Another approach, recently gaining attention, is the use of PageRank algorithms. While these descriptive approaches provide insight into networks with limited information, including small networks, there is, as yet, little research detailing a statistical approach for small networks. This article aims to contribute at the interface of Bayesian statistical inference and social network analysis by offering practicing social scientists a relatively straightforward Bayesian approach to account for uncertainty while conducting descriptive social network analysis. The emphasis is on computational feasibility and easy implementation using existing R packages, such as sna and rjags, that are available from the Comprehensive R Archive Network (https://cran.r-project.org/). We analyze a network comprising 18 websites from the US and UK to discern transnational identities, previously analyzed using descriptive graph theory with no uncertainty quantification, using fully Bayesian model-based inference.

中文翻译：

---

描述性社交网络的贝叶斯建模和不确定性量化

本文提出了一种简单且易于实现的贝叶斯方法，用于对小型描述性社交网络中的不确定性进行建模和量化。虽然在过去十年左右的时间里，分析网络的统计方法蓬勃发展，从社会科学到遗传学，但这些方法通常涉及复杂的随机模型，其估计需要网络中的大量结构和信息。在解析谱的另一端，有基于计算图论中的数量和公理的纯描述方法。在社交网络中，流行的描述性度量包括但不限于所谓的 Krackhardt 公理。另一种最近引起关注的方法是使用 PageRank 算法。虽然这些描述性方法提供了对信息有限的网络（包括小型网络）的洞察，但目前还很少有研究详细说明小型网络的统计方法。本文旨在通过为实践社会科学家提供一种相对简单的贝叶斯方法来解释不确定性，同时进行描述性社会网络分析，从而为贝叶斯统计推断和社会网络分析的接口做出贡献。重点是使用可从综合 R 存档网络 (https://cran.r-project.org/) 获得的现有 R 包（例如 sna 和 rjags）的计算可行性和轻松实现。我们分析了一个由来自美国和英国的 18 个网站组成的网络，以识别跨国身份，