29 citations · 246 across the 34 of their papers we have counts for
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math.PR2014★ 17 cited
Asymptotic structure and singularities in constrained directed graphs
David Aristoff, Lingjiong Zhu
We study the asymptotics of large directed graphs, constrained to have certain densities of edges and/or outward -stars. Our models are close cousins of exponential random graph…
math.PR2014★ 25 cited
On the phase transition curve in a directed exponential random graph model
David Aristoff, Lingjiong Zhu
We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the important statistical content of such models is given by the n…
math.PR2011★ 1 cited
Emergent structures in large networks
David Aristoff, Charles Radin
We consider a large class of exponential random graph models and prove the existence of a region of parameter space corresponding to multipartite structure, separated by a phase tr…