Explicit Bounds on the Entropy of Piecewise H\"{o}lder Graphon Models

The paper investigates the entropy of random graphs produced by piecewise Hölder continuous graphons. It establishes a convergence rate for the normalized entropy as graph size increases and outlines the main proof ideas, with full details in the appendix. Using this result, the authors derive explicit quantitative entropy bounds for both the stochastic block model and the random geometric graph model, moving beyond previous asymptotic statements.

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