Asymptotic Structure of Constrained Exponential Random Graph Models |
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Authors: | Lingjiong Zhu |
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Institution: | 1.Department of Mathematics,Florida State University,Tallahassee,USA |
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Abstract: | 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. |
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