  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.
