Considering the large-scale networks that can represent construction of components in a unit, a transportation system, a supply chain, a social network system, and so on, some nodes have similar topological structures and thus play similar roles in the network and system analysis, usually complicating the analysis and resulting in considerable duplicated computations. In this paper, we present a graph learning approach to define and identify structural similarity between the nodes in a network or the components in a network system. Based on the structural similarity, we investigate component clustering at various significance levels that represent different extents of similarity. We further specify a spectral-graph-wavelet based graph learning method to measure the structural similarity and present its application in easing computation load of evaluating system survival signature and system reliability. The numerical examples and the application show the insights of structural similarity and effectiveness of the graph learning approach. Finally, we discuss potential applications of the graph-learning based structural similarity and conclude that the proposed structural similarity, component clustering, and graph learning approach are effective in simplifying the complexity of the network systems and reducing the computational cost for complex network analysis.

考虑到可以代表一个单元，运输系统，供应链，社交网络系统等组成部分的大型网络，某些节点具有相似的拓扑结构，因此在网络和系统分析中起着相似的作用，通常会使分析复杂化，并导致大量重复的计算。在本文中，我们提出了一种图学习方法来定义和识别网络中的节点或网络系统中的组件之间的结构相似性。基于结构的相似性，我们研究了代表不同程度相似程度的不同显着性水平的组件聚类。我们进一步指定了一种基于谱图-小波的图学习方法来测量结构相似性，并提出其在减轻评估系统生存特征和系统可靠性的计算量方面的应用。数值示例和应用表明了图学习方法在结构相似性和有效性方面的见识。最后，我们讨论了基于图学习的结构相似性的潜在应用，并得出结论，所提出的结构相似性，组件聚类和图学习方法可有效简化网络系统的复杂性并降低复杂网络分析的计算成本。数值示例和应用表明了图学习方法在结构相似性和有效性方面的见识。最后，我们讨论了基于图学习的结构相似性的潜在应用，并得出结论，所提出的结构相似性，组件聚类和图学习方法可有效简化网络系统的复杂性并降低复杂网络分析的计算成本。数值示例和应用表明了图学习方法在结构相似性和有效性方面的见识。最后，我们讨论了基于图学习的结构相似性的潜在应用，并得出结论，所提出的结构相似性，组件聚类和图学习方法可有效简化网络系统的复杂性并降低复杂网络分析的计算成本。