有向网络中同步的粗粒度化
Coarse Graining for Synchronization in Directed Networks
摘要：
粗粒化模型是分析和可视化大规模网络的一种很有前途的方法。粗粒度网络需要保持与初始网络相同的统计特性和动力学行为。对于无向网络的粗粒化问题，已有一些方法被提出并取得了较好的效果，但对于有向网络的粗粒化问题的研究还缺乏考虑。本文提出了一种拓扑感知的粗粒化方法（TCG）对有向网络进行粗粒化。对Kuramoto模型在四种有向网络（包括树形网络和Barabási-Albert网络、Watts-Strogatz网络和Erdös-Rényi网络的变种）上进行同步的线性稳定性分析和数值模拟，发现该方法能有效地保持网络的同步性.
英文摘要：
Coarse graining model is a promising way to analyze and visualize large-scale networks. The coarse-grained networks are required to preserve the same statistical properties as well as the dynamic behaviors as the initial networks. Some methods have been proposed and found effective in undirected networks, while the study on coarse graining in directed networks lacks of consideration. In this paper, we proposed a Topology-aware Coarse Graining (TCG) 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-like networks and variants of Barabási-Albert networks, Watts-Strogatz networks and Erdös-Rényi networks, we find our method can effectively preserve the network synchronizability.
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