Sparse graph sequences, generalized graphon processes and signal processing

arxiv(2023)

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摘要
Graphons are limit objects of sequences of graphs, used to analyze the behavior of large graphs. Recently, graphon signal processing has been developed to study large graphs from the signal processing perspective. However, it has the shortcoming that any sparse sequence of graphs always converges to the zero graphon, and the resulting signal processing theory is trivial. In this paper, we propose a signal processing framework based on the theory of generalized graphons. The main ingredient is to use the stretched cut distance to compare graphons. Based on the theoretical results obtained in the paper, we describe how to apply the framework to study sparse sequences of graphs, which can be applied in practical scenarios.
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