Because of the important roles of the Internet and social networks in modern society, much attention has been paid to analyzing graphs with real-world network properties. One of the most prominent traits of many real-world networks is that their degree distribution follows the so-called power-law, usually with parameter \gamma between 2 and 3. Graphs with such degree distributions are sparse but have vertices with very large degrees. There are peculiarly few available methods to sample the realizations of exact degree distribution uniformly. One of them a newly developed exact uniform sampler by Gao and Wormald (SODA, 2018), based on the configuration model. This works when the parameter \gamma is > 2.8810. Another approach is a newly developed version of the switch Markov chains, which suitable to sample power-law degree sequences with parameter \gamma >2.

In this talk we will survey these results.

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