Using deterministic tourist walk as a small-world metric on Watts-Strogatz networks

TL;DR

This paper introduces a modified deterministic tourist walk method to classify networks and proposes a new small-world metric, achieving over 90% accuracy in distinguishing regular, random, and small-world networks.

Contribution

The paper develops a novel application of the deterministic tourist walk for network classification and introduces a new small-world metric based on this method.

Findings

The method achieves over 90% accuracy in network classification.

The proposed small-world metric effectively distinguishes small-world networks.

Results on real-world networks validate the metric's effectiveness.

Abstract

The Watts-Strogatz model (WS) has been demonstrated to effectively describe real-world networks due to its ability to reproduce the small-world properties commonly observed in a variety of systems, including social networks, computer networks, biochemical reactions, and neural networks. As the presence of small-world properties is a prevalent characteristic in many real-world networks, the measurement of "small-worldness" has become a crucial metric in the field of network science, leading to the development of various methods for its assessment over the past two decades. In contrast, the deterministic tourist walk (DTW) method has emerged as a prominent technique for texture analysis and network classification. In this paper, we propose the use of a modified version of the DTW method to classify networks into three categories: regular networks, random networks, and small-world networks. Additionally, we construct a small-world metric, denoted by the coefficient $\chi$, from the DTW method. Results indicate that the proposed method demonstrates excellent performance in the task of network classification, achieving over $90\%$ accuracy. Furthermore, the results obtained using the coefficient $\chi$ on real-world networks provide evidence that the proposed method effectively serves as a satisfactory small-world metric.