Phase transition in the two star Exponential Random Graph Model

2013/10/15 by Sumit Mukherjee, Mukherjee, Sumit
Computer Science · Mathematics · Physics and Astronomy · #05C80 #62P25 #Complex Network Analysis Techniques #FOS: Mathematics #Opinion Dynamics and Social Influence #Statistics Theory (math.ST) #Topological and Geometric Data Analysis #math.ST #msc:05C80 #msc:62P25 #stat.TH

paper · pdf · doi:10.48550/arxiv.1310.4164

21 pages, 7 figures

arxiv created 2013/10/15 · openalex publication_date 2013/10/15 · arxiv updated 2013/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper gives a way to simulate from the two star probability distribution on the space of simple graphs via auxiliary variables. Using this simulation scheme, the model is explored for various domains of the parameter values, and the phase transition boundaries are identified, and shown to be similar as that of the Curie-Weiss model of statistical physics. Concentration results are obtained for all the degrees, which further validate the phase transition predictions.

Citations

• The structure and function of complex networks
• An introduction to exponential random graph (p*) models for social networks

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