中文摘要：

复杂网络的中尺度研究是目前复杂网络研究中的一个前沿方向。本文主要介绍复杂网络的Laplacian矩阵的特征值谱的性质,指出特征值谱与度序列的强相关性。并且,在中尺度意义下,研究了不同拓扑结构的复杂网络的同步以及广义同步过程,发现同步是从度大的区域开始。进一步揭示了社团结构和同步时间尺度都与网络的特征值谱有关,社团网络的同步过程表现为部分同步—聚类同步—全局完全同步,该过程有助于网络社团结构的识别。最后介绍了与网络中尺度研究相关的一些前沿工作。

英文摘要：

Nowadays,mesoscales in complex networks has been an important topic of research in the field of complex networks.The paper presents the Laplacian spectral features of complex networks and reports the finding of a strong correlation between the laplacian spectrum and the node-degree sequence of a network.Furthermore,the synchronization and generalized synchronization of complex networks under different topological structures at the mesoscale level of description are studied.It is found that synchronization first starts from the nodes with largest degrees.It is also explored that the Laplacian spectrum shows a close relation with community structure and time scales regarding the network synchronization process.For community networks,there exists a general path towards synchronization： partial synchronization-cluster synchronization-global complete synchronization.This dynamical process helps to find the community structure of a network.Finally,some advanced researches of mesoscales in complex networks is introduced.