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Time-evolving random graph models have appeared and have been studied invarious fields of research over the past decades. However, the rigorousmathematical treatment of large graphs and their limits at the process-level isstill in its infancy. In this article, we adapt the approach of Athreya, denHollander and R\"ollin (2021+) to the setting of multigraphs and multigraphons,introduced by Kolossv\'ary and R\'ath (2011). We then generalise the work ofR\'ath (2012) and R\'ath and Szak\'acs (2012), who analysed edge-flippingdynamics on the configuration model -- in contrast to their work, we establishweak convergence at the process-level, and by allowing removal and addition ofedges, these limits are non-deterministic.

Dense multigraphon-valued stochastic processes and edge-changing dynamics in the configuration model