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- W4380993453 abstract "Random graph models are playing an increasingly important role in science and industry, and finds their applications in a variety of fields ranging from social and traffic networks, to recommendation systems and molecular genetics. In this paper, we perform an in-depth analysis of the random Kronecker graph model proposed in cite{leskovec2010kronecker}, when the number of graph vertices $N$ is large. Built upon recent advances in random matrix theory, we show, in the dense regime, that the random Kronecker graph adjacency matrix follows approximately a signal-plus-noise model, with a small-rank (of order at most $log N$) signal matrix that is linear in the graph parameters and a random noise matrix having a quarter-circle-form singular value distribution. This observation allows us to propose a ``denoise-and-solve'' meta algorithm to approximately infer the graph parameters, with reduced computational complexity and (asymptotic) performance guarantee. Numerical experiments of graph inference and graph classification on both synthetic and realistic graphs are provided to support the advantageous performance of the proposed approach." @default.
- W4380993453 created "2023-06-17" @default.
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- W4380993453 date "2023-06-14" @default.
- W4380993453 modified "2023-09-27" @default.
- W4380993453 title "Analysis and Approximate Inference of Large and Dense Random Kronecker Graphs" @default.
- W4380993453 doi "https://doi.org/10.48550/arxiv.2306.08489" @default.
- W4380993453 hasPublicationYear "2023" @default.
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