Abstract：

Coarse graining model is a promising way to analyze and visualize large-scale networks. The coarse-grained networks are required to preserve statistical properties as well as the dynamic behaviors of the initial networks. Some methods have been proposed and found effective in undirected networks, while the study on coarse graining directed networks lacks of consideration. In this paper, we proposed a Path-based Coarse Graining (PCG) method to coarse grain the directed networks. Performing the linear stability analysis of synchronization and numerical simulation of the Kuramoto model on four kinds of directed networks, including tree networks and variants of Barab´asi-Albert networks, Watts-Strogatz networks and Erdos-Renyi networks, we find our method can effectively preserve the network synchronizability.