In this article, we revisit and expand our prior work on graph similarity. As with our earlier work, we focus on a view of similarity which does not require node correspondence between graphs under comparison. Our work is suited to the temporal study of networks, change-point and anomaly detection and simple comparisons of static graphs. It provides a similarity metric for the study of (weakly) connected graphs. Our work proposes a metric designed to compare networks and assess the (dis)similarity between them. For example, given three different graphs with possibly different numbers of nodes, $G_1$, $G_2$ and $G_3$, we aim to answer two questions: a) "How different is $G_1 $ from $G_2$?" and b) "Is graph $G_3$ more similar to $G_1$ or to $G_2$?". We illustrate the value of our test and its accuracy through several new experiments, using synthetic and real-world graphs.

翻译：本文中，我们重新审视并扩展了先前在图相似性方面的研究工作。与早期工作一致，我们聚焦于一种无需比较图之间节点对应关系的相似性视角。本方法适用于网络的时序分析、变化点与异常检测以及静态图的简单比较，为（弱）连通图的研究提供了一种相似性度量。我们提出了一种旨在比较网络并评估其（不）相似性的度量方法。例如，给定三个可能具有不同节点数的图 $G_1$、$G_2$ 和 $G_3$，我们旨在回答两个问题：a) “$G_1$ 与 $G_2$ 的差异程度如何？”；b) “图 $G_3$ 更接近 $G_1$ 还是 $G_2$？”。我们通过使用合成图与真实世界图的多项新实验，展示了该检验方法的实用价值及其准确性。