2 research outputs found
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