  Many popular network models rely on the assumption of (vertex)
exchangeability, in which the distribution of the graph is invariant to
relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that
these graphs are dense or empty with probability one, whereas many real-world
graphs are sparse. We present an alternative notion of exchangeability for
random graphs, which we call edge exchangeability, in which the distribution of
a graph sequence is invariant to the order of the edges. We demonstrate that
edge-exchangeable models, unlike models that are traditionally vertex
exchangeable, can exhibit sparsity. To do so, we outline a general framework
for graph generative models; by contrast to the pioneering work of Caron and
Fox (2015), models within our framework are stationary across steps of the
graph sequence. In particular, our model grows the graph by instantiating more
latent atoms of a single random measure as the dataset size increases, rather
than adding new atoms to the measure.
