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

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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.