引入图累积量：你的社交网络的变化是什么？
Introducing Graph Cumulants: What is the Variance of Your Social Network?
摘要：
在一个日益相互关联的世界中，理解和总结这些网络的结构变得越来越重要。然而，这项任务是不平凡的;拟议的汇总统计是不同的网络，他们所描述的，和一个标准化的层次结构尚未建立。相反，向量值随机变量允许根据其累积量进行这样的描述（例如，均值、（协）方差、偏斜、峰度）。在这里，我们引入了网络累积量的自然模拟，基于越来越多的连接之间的相关性构建分层描述，无缝地结合额外的信息，如有向边，节点属性和边权重。这些图累积量提供了一个原则性和统一的框架，用于量化网络显示任何感兴趣的子结构（如测量聚类的集团）的倾向。此外，它们产生了网络的最大熵模型的自然分层家族（即，ERGMs），不遭受“简并问题”，一个共同的实际陷阱，其他ERGMs。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
