A statistical test for network similarity

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.