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Subsampling sparse graphons under minimal assumptions

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  • Robert Lunde
  • Purnamrita Sarkar

Abstract

SummaryWe study the properties of two subsampling procedures for networks, vertex subsampling and $p$-subsampling, under the sparse graphon model. The consistency of network subsampling is demonstrated under the minimal assumptions of weak convergence of the corresponding network statistics and an expected subsample size growing to infinity more slowly than the number of vertices in the network. Furthermore, under appropriate sparsity conditions, we derive limiting distributions for the nonzero eigenvalues of an adjacency matrix under the sparse graphon model. Our weak convergence result implies the consistency of our subsampling procedures for eigenvalues under appropriate conditions.

Suggested Citation

  • Robert Lunde & Purnamrita Sarkar, 2023. "Subsampling sparse graphons under minimal assumptions," Biometrika, Biometrika Trust, vol. 110(1), pages 15-32.
    • Handle: RePEc:oup:biomet:v:110:y:2023:i:1:p:15-32.
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    File URL: http://hdl.handle.net/10.1093/biomet/asac032
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