  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.
