A Detailed Investigation into Near Degenerate Exponential Random Graphs
Random graphs, Exponential family, Asymptotic graph structure, Degenerate
College of Natual Science and Mathematics, Mathematics
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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Yin, Mei. “A Detailed Investigation into Near Degenerate Exponential Random Graphs.” Journal of Statistical Physics, vol. 164, no. 1, 2016, pp. 241–253. doi: 10.1007/s10955-016-1539-3.