Lachgar Ahmed, Achahbar Abdelfattah
Condensed Matter Group, Department of Physics, Faculty of Sciences, Abdelmalek Essâadi University, Tétouan, Morocco.
Sci Rep. 2024 Mar 19;14(1):6555. doi: 10.1038/s41598-023-50651-x.
The small-world (SW) network model introduced by Watts and Strogatz has significantly influenced the study of complex systems, spurring the development of network science as an interdisciplinary field. The Newman-Watts model is widely applied to analyze SW networks by adding several randomly placed shortcuts to a regular lattice. We meticulously examine related previous works and conclude that the scaling of various pertinent quantities lacks convincing evidence. We demonstrate that the SW property primarily stems from the existence of clusters of nodes linked by shortcuts rather than just the mean number of shortcuts. Introducing the mean degree of clusters linked by shortcuts as a new key parameter resolves the scaling ambiguity, yielding a more precise characterization of the network. Our findings provide a new framework for analyzing SW networks, highlighting the significance of considering emergent structures in complex systems. We also develop a phase diagram of the crossover transition from the small to the large world, offering profound insights into the nature of complex networks and highlighting the power of emergence in shaping their behavior.
由瓦茨（Watts）和斯特罗加茨（Strogatz）提出的小世界（SW）网络模型对复杂系统的研究产生了重大影响，推动了网络科学作为一个跨学科领域的发展。纽曼 - 瓦茨（Newman - Watts）模型通过在规则晶格中添加几个随机放置的捷径被广泛应用于分析SW网络。我们仔细研究了之前的相关工作，并得出结论：各种相关量的标度缺乏令人信服的证据。我们证明，SW特性主要源于由捷径连接的节点簇的存在，而不仅仅是捷径的平均数量。引入由捷径连接的簇的平均度作为一个新的关键参数解决了标度的模糊性，从而对网络进行了更精确的表征。我们的研究结果为分析SW网络提供了一个新框架，突出了在复杂系统中考虑涌现结构的重要性。我们还绘制了从小世界到大世界的交叉转变相图，为复杂网络的本质提供了深刻见解，并突出了涌现现象在塑造其行为方面的力量。
