A statistical test for network similarity

TL;DR

This paper introduces a new statistical similarity metric for graphs that does not require node correspondence, useful for analyzing network evolution, anomalies, and static graph comparisons.

Contribution

It proposes a novel graph similarity metric capable of comparing graphs without node correspondence, expanding tools for network analysis.

Findings

The metric effectively distinguishes between different graphs.

It performs well on synthetic and real-world network data.

The method is applicable to temporal and static network comparisons.

Abstract

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.