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=== 谱方法 ===

=== 谱方法 ===

基于网络谱性质的方法通过保持特定过程动力学行为进行粗粒化。谱粗粒化最初用于研究网络随机游走，保留随机矩阵最大特征值及对应特征向量以保持大尺度行为，剔除快模态同时保留慢模态[26]，已推广至二部网络[27]和耦合振子同步动力学研究[28–30]，也用于有向网络同步[31]和可控性分析[32]。

基于网络谱性质的方法通过保持特定过程动力学行为进行粗粒化。谱粗粒化最初用于研究网络随机游走，保留随机矩阵最大特征值及对应特征向量以保持大尺度行为，剔除快模态同时保留慢模态<ref name="Gfeller_Spectral_coarse_graining">{{cite journal|author1=Gfeller D|author2=Los Rios P.|title=Spectral coarse graining of complex networks|journal=Phys. Rev. Lett.|year=2007|volume=99|url=}}</ref>，已推广至二部网络<ref name="Wang_Spectral_coarse_graining_bipartite">{{cite journal|author1=Wang Y|author2=Zeng A|author3=Di Z|author4=Fan Y.|title=Spectral coarse graining for random walks in bipartite networks|journal=Chaos|year=2013|volume=23|url=}}</ref>和耦合振子同步动力学研究<ref name="Gfeller_Spectral_synchronization">{{cite journal|author1=Gfeller D|author2=Los Rios P.|title=Spectral coarse graining and synchronization in oscillator networks|journal=Phys. Rev. Lett.|year=2008|volume=100|url=}}</ref><ref name="Chen_Spectral_coarse_graining_clustered">{{cite journal|author1=Chen J|author2=an Lu J|author3=Lu X|author4=Wu X|author5=Chen G.|title=Spectral coarse graining of complex clustered networks|journal=Commun. Nonlinear Sci. Numer. Simul.|year=2013|volume=18|url=}}</ref><ref name="Jia_Optimization_algorithms_SCG">{{cite journal|author1=Jia Z|author2=Zeng L|author3=Wang Y.-Y.|author4=Wang P.|title=Optimization algorithms for spectral coarse-graining of complex networks|journal=Physica A|year=2019|volume=514|url=}}</ref>，也用于有向网络同步<ref name="Zeng_Coarse_graining_synchronization">{{cite journal|author1=Zeng A|author2=Lü L.|title=Coarse graining for synchronization in directed networks|journal=Phys. Rev. E|year=2011|volume=83|url=}}</ref>和可控性分析<ref name="Wang_Spectral_controllability">{{cite journal|author1=Wang P|author2=Xu S.|title=Spectral coarse grained controllability of complex networks|journal=Physica A|year=2017|volume=478|url=}}</ref>。

 

=== 拓扑方法 ===

=== 拓扑方法 ===