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Rubin‐Delanchy P, Cape J, Tang M, Priebe CE. A statistical interpretation of spectral embedding: The generalised random dot product graph. J R Stat Soc Series B Stat Methodol 2022. [DOI: 10.1111/rssb.12509] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
| | - Joshua Cape
- University of Pittsburgh Pittsburgh Pennsylvania USA
| | - Minh Tang
- North Carolina State University Raleigh North Carolina USA
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Lunde R, Sarkar P. Subsampling Sparse Graphons Under Minimal Assumptions. Biometrika 2022. [DOI: 10.1093/biomet/asac032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Summary
We 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 corresponding network statistics and an (expected) subsample size growing to infinity slower 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.
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Affiliation(s)
- Robert Lunde
- University of Michigan Department of Statistics, , Ann Arbor, Michigan 48109, U.S.A
| | - Purnamrita Sarkar
- University of Texas Austin Department of Statistics and Data Sciences, , Texas 78712, U.S.A
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