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83 best power-law fit using the maximum likelihood method [33]. Table 5.2 shows the estimated power-law coefficient along with the Kolmogorov-Smirnov goodness-of-fit metric [33]. While the best power-law coefficients approximate the distributions very well for Flickr, LiveJournal, and YouTube, the Orkut data deviates significantly. Two factors contribute to this deviation. First, our Orkut crawl reached only 11.3% of the network — partial BFS crawls tend to undersample nodes with lower degree, which can explain the flat head of the distribution [85]. Second, both Live- Journal and Orkut artificially cap a user’s number of outgoing links,1 which leads to a distortion in the distribution for high degrees. Outdegree Indegree Network α D α D Web [23] 2.67 Flickr 1.74 LiveJournal 1.59 Orkut 1.50 YouTube 1.63 - 2.09 0.0575 1.78 0.0783 1.65 0.6319 1.50 0.1314 1.99 - 0.0278 0.1037 0.6203 0.0094 Table 5.2 : Power-law coefficient estimates (α) and corresponding Kolmogorov- Smirnov goodness-of-fit metrics (D). The Flickr, LiveJournal, and YouTube networks are well approximated by a power-law. 1Orkut caps the outdegree at 1,000, and LiveJournal at 750. Both of these caps were instituted after the networks were established, and some users therefore exceed the caps. Also, Flickr has since instituted a cap of 3,000 non-reciprocal links; however, the data shown here was collected before this cap was established.PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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