Abstract.

Because of the important roles of the Internet and social networks in modern society, much attention has been paid to analyzi ng graphs with real-world network properties. One of the most prominent tra its of many real-world networks is that their degree distribution follows t he so-called power-law, usually with parameter \gamma between 2 and 3. Grap hs with such degree distributions are sparse but have vertices with very la rge degrees.

There are peculiarly few available methods to sample the r ealizations of exact degree distribution uniformly. One of them a newly dev eloped exact uniform sampler by Gao and Wormald (SODA, 2018), based on the configuration model. This works when the parameter \gamma is > 2.8810. Anot her approach is a newly developed version of the switch Markov chains, whic h suitable to sample power-law degree sequences with parameter \gamma >2. DTSTAMP:20210621T020219Z DTSTART;TZID=Europe/Budapest:20190412T103000 DTEND;TZID=Europe/Budapest:20190412T123000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR