论文标题
介绍图累积物：您的社交网络的差异是什么？
Introducing Graph Cumulants: What is the Variance of Your Social Network?
论文作者
论文摘要
在越来越多的相互联系的世界中，理解和总结这些网络的结构变得越来越相关。但是，这项任务是不平凡的。拟议的摘要统计数据与他们描述的网络一样多样化，尚未建立标准化的层次结构。相比之下，矢量值随机变量承认了这种描述，其累积剂（例如平均值，（CO）方差，偏斜，峰度）。在这里，我们介绍了网络累积物的自然类似物，基于越来越多的连接之间的相关性构建层次描述，无缝包含其他信息，例如定向边缘，节点属性和边缘重量。这些图累积物提供了一个有原则的统一框架，用于量化网络倾向以显示任何感兴趣的子结构（例如测量聚类的集团）。此外，它们产生了一个自然的网络最大熵模型（即ERGMS）的自然等级家族，这些模型不会遭受“退化问题”的困扰，这是其他ERGMS的常见实际陷阱。
In an increasingly interconnected world, understanding and summarizing the structure of these networks becomes increasingly relevant. However, this task is nontrivial; proposed summary statistics are as diverse as the networks they describe, and a standardized hierarchy has not yet been established. In contrast, vector-valued random variables admit such a description in terms of their cumulants (e.g., mean, (co)variance, skew, kurtosis). Here, we introduce the natural analogue of cumulants for networks, building a hierarchical description based on correlations between an increasing number of connections, seamlessly incorporating additional information, such as directed edges, node attributes, and edge weights. These graph cumulants provide a principled and unifying framework for quantifying the propensity of a network to display any substructure of interest (such as cliques to measure clustering). Moreover, they give rise to a natural hierarchical family of maximum entropy models for networks (i.e., ERGMs) that do not suffer from the "degeneracy problem", a common practical pitfall of other ERGMs.
