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84 Additionally, we tested the stability of the power-law coefficient estimates by running the maximum likelihood estimator over varyingly sized subsamples of our data [162]. We found that the estimates of the power-law coefficient were remarkably stable; the estimates varied by less than 6% from those provided in Table 5.2 when we considered as few as 1,000 data points. Table 5.2 also shows a difference between the structure of social networks and that of previously observed networks. In the Web, for example, the indegree and outdegree power-law exponents have been shown to differ significantly, while the power-law exponents for the indegree and outdegree distributions in each of our social networks are very similar. This implies that in online social networks, the distribution of outgoing links is similar to that of incoming links, while in the Web, the incoming links are significantly more concentrated on a few high-degree nodes than the outgoing links. 1 0.8 0.6 0.4 0.2 0 Figure 5.3 : Plot of the distribution of links across nodes. Social networks show similar distributions for outgoing and incoming links, whereas the Web links shows different distributions. Web In Flickr Out / In Web Out 0 0.2 0.4 0.6 0.8 1 Fraction of Users Fraction of LinksPDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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