Phase Transitions in Edge-weighted Exponential Random Graphs: Near-degeneracy and Universality

Authors

Ryan DeMuse, University of Denver
Danielle Larcomb, University of Denver
Mei Yin, University of DenverFollow

Publication Date

2-28-2018

Document Type

Article

Organizational Units

Mathematics

Keywords

Exponential random graphs, Edge-weighted, Near-degeneracy, 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 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.

Publication Statement

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Recommended Citation

DeMuse, Ryan, et al. “Phase Transitions in Edge-Weighted Exponential Random Graphs: Near-Degeneracy and Universality.” Journal of Statistical Physics, vol. 171, no. 1, 2018, pp. 127–144. doi: 10.1007/s10955-018-1991-3.