Synchronization in collaboration network

Cooperative relationship in social network can be described effectively by one-mode RDP model (?RDP? represents the initials of Ramasco, Dorogovtsev and Pastor-Satorras, who propose the model.), where n > 2 participants including m?1 new participants and n -m > 1 ?old? participants collaborate on one project together at each time step. In this paper, the synchronization in this evolution network model is studied systematically. We discover that the synchronization capacity of one-mode RDP model is independent of the network size N, can be reduced by slightly increasing m when m is small, and also be increased by increasing n -m. By calculating the specific expression of average path length (APL) of one-mode RDP model, we analyze the correlation between APL and synchronizability of this model. In some cases, there is no correlation between the APL and the synchronizability of one-mode RDP model. But when N and m are fixed, as n -m increases, the synchronizability of this model is negatively correlated with APL. Furthermore, we explore the robustness and fragility of synchronization in one-mode RDP model. The synchronizability of this model against random fault is not correlated with m and N, and the synchronizability to resist intentional attack is independent of m and N. The synchronizability of this model against random fault and intentional attack can be improved by increasing n -m. Our study fills in the gaps of previous studies that did not consider the synchronization and average path length of one-mode RDP model. Our research results also contain the previous relevant research results and expand them.