A detailed investigation into near degenerate exponential random graphs

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.Comment: 15 pages, 3 figures, 2 table

Phase transitions in exponential random graphs

We derive the full phase diagram for a large family of two-parameter exponential random graph models, each containing a first order transition curve ending in a critical point.Comment: Published in at http://dx.doi.org/10.1214/12-AAP907 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Foreign Reserves and Economic Growth: Granger Causality Analysis with Panel Data

This paper will investigate the Granger causality between foreign reserves and economic growth in twenty largest reserves-holding countries ranging from 1980 to 2008. The method of first-differencing each variable is used to estimate the panel data VAR equations for Granger causality test. The results show the foreign reserves unilaterally Granger cause economic growth only in the emerging countries. In the advanced countries, there is no Granger causal relation between foreign reserves and economic growth.

Phase Transitions in Edge-Weighted Exponential Random Graphs: Near-Degeneracy and Universality

Conventionally used exponential random graphs cannot directly model weighted networks as the underlying probability space consists of simple graphs only. Since many substantively important networks are weighted, this limitation is especially problematic. We extend the existing exponential framework by proposing a generic common distribution for the edge weights. Minimal assumptions are placed on the distribution, that is, it is non-degenerate and supported on the unit interval. By doing so, we recognize the essential properties associated with near-degeneracy and universality in edge-weighted exponential random graphs.Comment: 15 pages, 4 figures. This article extends arXiv:1607.04084, which derives general formulas for the normalization constant and characterizes phase transitions in exponential random graphs with uniformly distributed edge weights. The present article places minimal assumptions on the edge-weight distribution, thereby recognizing essential properties associated with near-degeneracy and universalit