tag:blogger.com,1999:blog-6894866515532737257.post2241041211143382698..comments2024-03-27T01:01:09.785-07:00Comments on Probably Overthinking It: It's a small world, scale-free network after allAllen Downeyhttp://www.blogger.com/profile/01633071333405221858noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6894866515532737257.post-91060316911878996462016-09-16T08:22:25.195-07:002016-09-16T08:22:25.195-07:00That's very helpful. Thanks!That's very helpful. Thanks!Allen Downeyhttps://www.blogger.com/profile/01633071333405221858noreply@blogger.comtag:blogger.com,1999:blog-6894866515532737257.post-80902387206358174252016-09-15T02:35:42.551-07:002016-09-15T02:35:42.551-07:00I enjoyed this blog post very much. I didn't t...I enjoyed this blog post very much. I didn't think about scale free networks for some years. However, I see some waek points:<br />- the only parameter that alows you to controll the degree sequence and the clustering coefficient independently of the average degree is the rewiring probability. this means that the clustering coefficient and the distribution do strongly dependend on each other. <br />-every edge is part of a triangle. <br /><br />There is a the model of hyperbolic randomg raphs which became very popular in the last few years. Its possible to control its clustering, average degree and degree sequence. The degree sequence can be power law distributed, the clustering can be strong and the average degree can be small. The model was introduced here:<br />http://arxiv.org/pdf/1006.5169.pdf<br />Later we analyzed it rigorously here: http://arxiv.org/pdf/1205.1470.pdf<br /><br />Since then many other usefull properties like small average path lengh, efficient greedy routing etc. have been proven. Moreover, on a phylosophical level, it give (in my opinion) a very nice explanation for the properties of social networks, the internet graphs and other small world network. <br />Anonymoushttps://www.blogger.com/profile/07399700772199193833noreply@blogger.com