Structure properties and synchronizability of cobweb-like networks

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.