An Lp theory of sparse graph convergence I: Limits, sparse random graph models, and power law distributions
Name
S0002-9947-2019-07543-8.pdf
Description
Published version
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525.82 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Borgs, Christian
Chayes, Jennifer
Cohn, Henry
Zhao, Yufei
Date Issued
May 2019
Journal
Transactions of the American Mathematical Society
Publisher
American Mathematical Society (AMS)
Citation
Borgs, Christian et al. “An Lp theory of sparse graph convergence I: Limits, sparse random graph models, and power law distributions.” Transactions of the American Mathematical Society, vol. 372, no. 5, 2019, pp. 3019-3062 © 2019 The Author(s)
Version
Final published version
Abstract
We introduce and develop a theory of limits for sequences of sparsegraphs based on Lp graphons, which generalizes both the existing L∞ theory ofdense graph limits and its extension by Bollob ́as and Riordan to sparse graphswithout dense spots. In doing so, we replace the no dense spots hypothesiswith weaker assumptions, which allow us to analyze graphs with power lawdegree distributions. This gives the first broadly applicable limit theory forsparse graphs with unbounded average degrees. In this paper, we lay the foun-dations of the Lp theory of graphons, characterize convergence, and developcorresponding random graph models, while we prove the equivalence of severalalternative metrics in a companion paper.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1090/TRAN/7543
