Phase Transitions in EdgeWeighted Exponential Random Graphs: NearDegeneracy and Universality
Abstract
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 nondegenerate and supported on the unit interval. By doing so, we recognize the essential properties associated with neardegeneracy and universality in edgeweighted exponential random graphs.
 Publication:

Journal of Statistical Physics
 Pub Date:
 April 2018
 DOI:
 10.1007/s1095501819913
 arXiv:
 arXiv:1706.02163
 Bibcode:
 2018JSP...171..127D
 Keywords:

 Mathematics  Probability;
 Mathematical Physics
 EPrint:
 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 edgeweight distribution, thereby recognizing essential properties associated with neardegeneracy and universality