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arXiv · 2401.05326

Reply to 'Comments on Graphon Signal Processing' [arXiv:2310.14683]

Luana Ruiz·Luiz F. O. Chamon·Alejandro Ribeiro
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Abstract

This technical note addresses an issue [arXiv:2310.14683] with the proof (but not the statement) of [arXiv:2003.05030, Proposition 4]. The statement of the proposition is correct, but the proof as written in [arXiv:2003.05030] is not and due to a typo in the manuscript, a reference to the correct proof is effectively missing. In the sequel, we present [arXiv:2003.05030, Proposition 4] and its proof. The proof follows from results in [2] that we reproduce here for clarity of exposition. Since the statement of the proposition remains correct, no change in the results of [arXiv:2003.05030] are required. In particular, Lemma 3 and Lemma 4 showing spectral convergence of graphs to graphons, Theorem 1 showing convergence of the GFT to the WFT, and Theorems 3 and 4 showing convergence of graph to graphon filters, remain valid.

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Luana Ruiz, Luiz F. O. Chamon, Alejandro Ribeiro. 2024-01-05. Reply to 'Comments on Graphon Signal Processing' [arXiv:2310.14683]. https://arxiv.org/abs/2401.05326

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