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：我们提供了指数随机图模型（ERGM）理论中的基础结果的简化证明，即当目标统计量位于可实现统计量集合的凸壳的相对内部时，最大似然估计存在。