Asymptotic structure and singularities in constrained directed graphs

作者：Aristoff David; Zhu Lingjiong^*

来源：Stochastic Processes and Their Applications, 2015, 125(11): 4154-4177.

DOI：10.1016/j.spa.2015.06.004

• Dense random graphs
• Exponential random graphs
• Graph limits
• Entropy
• Phase transitions

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.

• 出版日期2015-11