Random graph models are widely used to understand network properties and graph algorithms. Key to such analyses are the different parameters of each model, which affect various network features, such as its size, clustering, or degree distribution. The exact effect of the parameters on these features is not well understood, mainly because we lack tools to thoroughly investigate this relation. Moreover, the parameters cannot be considered in isolation, as changing one affects multiple features. Existing approaches for finding the best model parameters of desired features, such as a grid search or estimating the parameter-feature relations, are not well suited, as they are inaccurate or computationally expensive. We introduce an efficient iterative fitting method, named ParFit, that finds parameters using only a few network samples, based on the Robbins-Monro algorithm. We test ParFit on three well-known graph models, namely Erd\H{o}s-R\'enyi, Chung-Lu, and geometric inhomogeneous random graphs, as well as on real-world networks, including web networks. We find that ParFit performs well in terms of quality and running time across most parameter configurations.

翻译：随机图模型被广泛用于理解网络特性和图算法。这类分析的关键在于每个模型中影响网络特征（如规模、聚类系数或度分布）的不同参数。参数对这些特征的确切影响机制尚不明确，主要原因是缺乏系统性探究该关系的工具。此外，参数无法孤立考虑——改变一个参数会影响多个网络特征。现有方法（如网格搜索或参数-特征关系估计）在寻找符合目标特征的最佳模型参数时存在精度不足或计算成本高昂的缺陷。我们提出一种基于Robbins-Monro算法的高效迭代拟合方法ParFit，该方法仅需少量网络样本即可完成参数拟合。在三个经典图模型（Erdős-Rényi、Chung-Lu和几何异质随机图）及包含万维网在内的真实网络上的实验表明，ParFit在大多数参数配置中均展现出优异的拟合质量与运行效率。