Article ID Journal Published Year Pages File Type
10527180 Stochastic Processes and their Applications 2015 24 Pages PDF
Abstract
We study the asymptotics of large directed graphs, constrained to have certain densities of edges and/or outward p-stars. Our models are close cousins of exponential random graph models, in which edges and certain other subgraph densities are controlled by parameters. We find that large graphs have either uniform or bipodal structure. When edge density (resp. p-star density) is fixed and p-star density (resp. edge density) is controlled by a parameter, we find phase transitions corresponding to a change from uniform to bipodal structure. When both edge and p-star density are fixed, we find only bipodal structures and no phase transition.
Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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