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A Detailed Investigation into Near Degenerate Exponential Random Graphs

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Abstract

The exponential family of random graphs has been a topic of continued research interest. Despite the relative simplicity, these models capture a variety of interesting features displayed by large-scale networks and allow us to better understand how phases transition between one another as tuning parameters vary. As the parameters cross certain lines, the model asymptotically transitions from a very sparse graph to a very dense graph, completely skipping all intermediate structures. We delve deeper into this near degenerate tendency and give an explicit characterization of the asymptotic graph structure as a function of the parameters.

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Acknowledgments

The author is very grateful to the anonymous referees for the invaluable suggestions that greatly improved the quality of this paper. She appreciated the opportunity to talk about this work in the Special Session on Topics in Probability at the 2016 AMS Western Spring Sectional Meeting, organized by Tom Alberts and Arjun Krishnan. Mei Yin’s research was partially supported by NSF Grant DMS-1308333.

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  1. Department of Mathematics, University of Denver, Denver, CO, 80208, USA

    Mei Yin

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  1. Mei Yin
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Yin, M. A Detailed Investigation into Near Degenerate Exponential Random Graphs. J Stat Phys 164, 241–253 (2016). https://doi.org/10.1007/s10955-016-1539-3

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  • DOI: https://doi.org/10.1007/s10955-016-1539-3

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