  We study a recent model for edge exchangeable random graphs introduced by
Crane and Dempsey; in particular we study asymptotic properties of the random
simple graph obtained by merging multiple edges. We study a number of examples,
and show that the model can produce dense, sparse and extremely sparse random
graphs. One example yields a power-law degree distribution. We give some
examples where the random graph is dense and converges a.s. in the sense of
graph limit theory, but also an example where a.s. every graph limit is the
limit of some subsequence. Another example is sparse and yields convergence to
a non-integrable generalized graphon defined on $(0,\infty)$.
