The cobweb-like network was constructed, and its structure properties and synchronizability were studied by numerical simulation and probability theory. For cobweb-like networks, the behaviors of structure properties with the adding probability are similar to those for the small-world network. However, the properties of cobweb-like networks also distinctly depend on the spoke–ring ratio r. With increasing r, the average path length decreases, and the average clustering coefficient increases. Simultaneously, the connectivity distribution becomes heterogeneous. Moreover, in the case of bounded synchronized region, the synchronizability shows complicated behaviors with r, and is enhanced favorably at r=2.28 with homogeneous load distribution. The reason is that homogeneous load distribution has an advantage over the communication between oscillators, which efficiently leads to global synchronization. This work could be useful for design and kinetic property research of cobweb-like networks.

中文翻译：

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蛛网状网络的结构性质和同步性

构建了蛛网状网络，利用数值模拟和概率论研究了其结构性质和同步性。对于蛛网状网络，结构属性的增加概率行为与小世界网络类似。然而，蛛网状网络的特性也明显取决于辐条环比 r。随着r的增加，平均路径长度减小，平均聚类系数增加。同时，连接分布变得异构。此外，在有界同步区域的情况下，同步性随着 r 表现出复杂的行为，并且在 r=2.28 时具有良好的增强效果，负载分布均匀。原因是均匀的负载分布比振荡器之间的通信具有优势，这有效地导致了全局同步。这项工作可用于蛛网状网络的设计和动力学特性研究。