Asymptotic Structure of Constrained Exponential Random Graph Models

In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that there exists non-trivial regions in the phase plane where the asymptotic structure is uniform and there also exists non-tri...

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Bibliographic Details
Published in:Journal of statistical physics 2017-03, Vol.166 (6), p.1464-1482
Main Author: Zhu, Lingjiong
Format: Article
Language:English
Subjects:
Analysis
Asymptotic properties
Constraint modelling
Mathematical and Computational Physics
Phase transitions
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Social networks
Statistical Physics and Dynamical Systems
Theoretical
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Summary:In this paper, we study exponential random graph models subject to certain constraints. We obtain some general results about the asymptotic structure of the model. We show that there exists non-trivial regions in the phase plane where the asymptotic structure is uniform and there also exists non-trivial regions in the phase plane where the asymptotic structure is non-uniform. We will get more refined results for the star model and in particular the two-star model for which a sharp transition from uniform to non-uniform structure, a stationary point and phase transitions will be obtained.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-017-1733-y