边加权指数随机图中的相变：近简并性与普适性
概率论
2019-06-10 v2 数学物理
math.MP
摘要
传统使用的指数随机图无法直接对加权网络建模，因为其底层的概率空间仅由简单图构成。由于许多具有实质性重要意义的网络是加权的，这一局限性尤为突出。我们通过为边权重提出一个通用的共同分布来扩展现有的指数框架。对该分布施加了极少的假设，即它是非退化的且支撑在单位区间上。通过这样做，我们识别了边加权指数随机图中与近简并性和普适性相关的基本性质。
引用
@article{arxiv.1706.02163,
title = {Phase Transitions in Edge-Weighted Exponential Random Graphs: Near-Degeneracy and Universality},
author = {Ryan DeMuse and Danielle Larcomb and Mei Yin},
journal= {arXiv preprint arXiv:1706.02163},
year = {2019}
}
备注
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 universality