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

Time-evolving random graph models have appeared and have been studied in various fields of research over the past decades. However, the rigorous mathematical treatment of large graphs and their limits at the process-level is still in its infancy. In this article, we adapt the approach of Athreya, den ting of multigraphs and multigraphons, introduced by Kolossvary and Rath (Acta Math. Hungar. 130 (2011) 1-34). We then generalise the work of Rath namics on the configuration model-in contrast to their work, we establish weak convergence at the process-level, and by allowing removal and addition of edges, these limits are nondeterministic.