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We introduce the exchangeable rewiring process for modeling time-varying networks. The process fulfills fundamental mathematical and statistical properties and can be easily constructed from the novel operation of random rewiring. We derive basic properties of the model, including consistency under subsampling, exchangeability, and the Feller property. A reversible sub-family related to the Erd\H{o}s-R'{e}nyi model arises as a special case.

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