Exploiting structural similarity in network reliability analysis using graph learning

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.