Dynamic Random Networks and Their Graph Limits

We study a broad class of stochastic process models for dynamic networks whose behavior satisfies the minimal regularity conditions of (i) exchangeability and (ii) càdlàg sample paths. Our main theorems characterize these processes through their induced behavior in the space of graph limits. Under the assumption of time-homogeneous Markovian dependence, we classify the discontinuities of these processes into three types, prove bounded variation of the sample paths in graph limit space, and express the process as a mixture of timeinhomogeneous, exchangeable Markov processes with càdlàg sample paths.