In defence of the simple: Euclidean distance for comparing complex networks

TL;DR

This paper demonstrates that the simple Euclidean distance is an effective and efficient metric for comparing complex networks, outperforming more complicated methods in distinguishing network differences.

Contribution

The study shows that Euclidean distance is a competitive and computationally efficient metric for network comparison, challenging the need for complex alternatives.

Findings

Euclidean distance effectively captures network differences

Simple metrics outperform complex methods in efficiency

Euclidean distance is suitable for real-world network analysis

Abstract

To improve our understanding of connected systems, different tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the graph comparison problem. Although different estimates exist to quantify how different two networks are, an appropriate metric has not been proposed. Within this framework we compare the performances of different networks distances (a topological descriptor and a kernel-based approach) with the simple Euclidean metric. We define the performance of metrics as the efficiency of distinguish two network's groups and the computing time. We evaluate these frameworks on synthetic and real-world networks (functional connectomes from Alzheimer patients and healthy subjects), and we show that the Euclidean distance is the one that efficiently captures networks differences in comparison to other proposals. We conclude that the operational use of complicated methods can be justified only by showing that they out-perform well-understood traditional statistics, such as Euclidean metrics.