  Desirable random graph models (RGMs) should (i) be tractable so that we can
compute and control graph statistics, and (ii) generate realistic structures
such as high clustering (i.e., high subgraph densities). A popular category of
RGMs (e.g., Erdos-Renyi and stochastic Kronecker) outputs edge probabilities,
and we need to realize (i.e., sample from) the edge probabilities to generate
graphs. Typically, each edge (in)existence is assumed to be determined
independently. However, with edge independency, RGMs theoretically cannot
produce high subgraph densities unless they "replicate" input graphs. In this
work, we explore realization beyond edge independence that can produce more
realistic structures while ensuring high tractability. Specifically, we propose
edge-dependent realization schemes called binding and derive closed-form
tractability results on subgraph (e.g., triangle) densities in graphs generated
with binding. We propose algorithms for graph generation with binding and
parameter fitting of binding. We empirically validate that binding exhibits
high tractability and generates realistic graphs with high clustering,
significantly improving upon existing RGMs assuming edge independency.
