  Empirical evidence suggests that heavy-tailed degree distributions occurring
in many real networks are well-approximated by power laws with exponents $\eta$
that may take values either less than and greater than two. Models based on
various forms of exchangeability are able to capture power laws with $\eta <
2$, and admit tractable inference algorithms; we draw on previous results to
show that $\eta > 2$ cannot be generated by the forms of exchangeability used
in existing random graph models. Preferential attachment models generate power
law exponents greater than two, but have been of limited use as statistical
models due to the inherent difficulty of performing inference in
non-exchangeable models. Motivated by this gap, we design and implement
inference algorithms for a recently proposed class of models that generates
$\eta$ of all possible values. We show that although they are not exchangeable,
these models have probabilistic structure amenable to inference. Our methods
make a large class of previously intractable models useful for statistical
inference.
