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。虽然自20世纪50年代以来，简单的随机图模型得到了很好的探索，但现代随机图模型却不那么容易分析。特别是，它们的预期结构（尚未）用封闭公式描述，需要通过抽样来探索。这个样本的生成及其分析在计算上是如此昂贵，以至于大型网络无法正确处理。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通过封闭公式近似估计结构。

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.