I have a question that I need at some point my research. Suppose that the upper-triangular entries of an $n\times n$ symmetric matrix $A$ are i.i.d. Uniform$(0,1)$. Does the weighted graph with weighted adjacency $A$ converge to a graphon as $n\rightarrow \infty$, and if so, how does the limiting graphon look like? Also, can the uniform distribution be generalized to some other distributions? Thanks in advance!
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$\begingroup$ What is a graphon? $\endgroup$– Jose Arnaldo BebitaCommented Aug 26, 2023 at 13:40
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1$\begingroup$ @JoseArnaldoBebitaDris: See en.wikipedia.org/wiki/Graphon $\endgroup$– Sam HopkinsCommented Aug 27, 2023 at 23:29
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$\begingroup$ For weighted graphs we use the notion of probability graphons instead: arxiv.org/pdf/2312.15935. The linked paper should give you all the information you need to solve this problem. $\endgroup$– TheBestMagicianCommented Oct 8 at 17:09
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