For large dense weighted SIS networks, prediction of epidemic curves is uniformly stable under trajectory-fitting error, while network reconstruction is provably non-identifiable in the cut norm.
A sampling construction of graphon 1-norm convergence
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abstract
In the short note, we describe a sampling construction that yields a sequence of graphons converging to a prescribed limit graphon in 1-norm. This convergence is stronger than the convergence in the cut norm, usually used to study graphon sequences. The note also contains errata of the previous version of the note.
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Why is it easier to predict the epidemic curve than to reconstruct the underlying contact network?
For large dense weighted SIS networks, prediction of epidemic curves is uniformly stable under trajectory-fitting error, while network reconstruction is provably non-identifiable in the cut norm.