We present a streamlined proof of the foundational result in the theory of exponential random graph models (ERGMs) that the maximum likelihood estimate exists if and only if the target statistic lies in the relative interior of the convex hull of the set of realizable statistics. .

翻译：我们给出了指数随机图模型（ERGM）理论中一个基础结果的精简证明：最大似然估计存在当且仅当目标统计量位于可实现统计量集合的凸包的相对内部。