Phase Transitions and Mean-Field Approaches for the efficient computation of expected properties of the Fixed Degree Sequence Model

为了从生物学、生态学和经济学的角度分析和评估现实世界网络中观察到的结构，有必要与所谓的随机图模型进行统计比较。虽然简单的随机图模型自20世纪50年代以来得到了很好的探索，但现代随机图模型并不容易分析。特别是，它们的预期结构（尚未）由封闭公式描述，需要通过采样来探索。生成这个样本及其分析的计算成本如此之高，以至于无法正确处理大型网络。在这个项目中，我们专注于统计物理的新方法，以加速样本的生成，并找到一种新的方法来近似估计的结构封闭的公式。

To analyze and assess observed structures in real-world networks from biology, ecology, and economics, a statistical comparison with so-called random graph models is necessary. While simple random graph models are well explored since the 1950s, modern random graph models are not as easily analyzable. Especially, their expected structures are not (yet) described by closed formulas and need to be explored by sampling. Generation of this sample and its analysis is computationally so costly that big networks cannot be properly processed. In this project we focus on new approaches from statistical physics, to accelerate the generation of the sample and to find a new approach in approximating estimated structures by closed formulas.