  This paper shows the equivalence class definition of graphons hinders a
direct development of dynamics on the graphon space, and hence proposes a
state-driven approach to obtain dynamic graphons. The state-driven dynamic
graphon model constructs a time-index sequence of the permutation-invariant
probability measures on the universal graph space by assigning i.i.d. state
random processes to $\mathbbm{N}$ and edge random variables to each of the
unordered integer pairs. The model is justified from three perspectives: graph
limit definition preservation, genericity, and analysis availability. It
preserves the graph limit definition of graphon by applying a bijection between
the permutation-invariant probability measures on the universal graph space and
the graphon space to obtain the dynamic graphon, where the existence of the
bijection is proved. Also, a generalized version of the model is proved to
cover the graphon space by an application of the celebrated Aldous-Hoover
representation, where generalization is achieved by adding randomness to the
edge-generating functions. Finally, analysis of the behavior of the dynamic
graphon is shown to be available by making assumptions on the state random
processes and the edge random variables.
