We define the edge reconnecting model, a random multigraph evolving in time. At each time step we change one endpoint of a uniformly chosen edge: the new endpoint is chosen by linear preferential attachment. We consider a sequence of edge reconnecting models where the sequence of initial multigraphs is convergent in a sense which is a natural generalization of the Lovász-Szegedy notion of convergence of dense graph sequences. We investigate how the limit objects evolve under the edge reconnecting dynamics if we rescale time properly: we give the complete characterization of the time evolution of the limiting object from its initial state up to the stationary state using the theory of exchangeable arrays, the Pólya urn model, queuing and diffusion processes. The number of parallel edges and the degrees evolve on different timescales and because of this the model exhibits “aging”.
