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108 current degree. To examine whether preferential attachment predicts the observed growth data, we calculated how the number of new links per day varies with the node degree. If preferential attachment is taking place, we would expect to see a positive correlation between the degree of a node and the number of new links it creates or receives. However, it is important to note that a positive correlation is a necessary but not sufficient condition for the validity of the preferential attachment mechanism, as other mechanisms could also result in such a correlation. For example, the “connecting nearest neighbors” model [154] has been shown to also exhibit such a correlation. 100 10 1 0.1 0.01 0.001 0.0001 Figure 6.2 : Log-log plot of outdegree versus number of new links per day. All networks show strong evidence of preferential attachment. Figure 6.4 plots this distribution in log-log scale for each of the five networks we studied. For the three directed graphs, we separately plot the number of new links created and received, with respect to the node’s current outdegree and indegree. 1 10 100 1000 1 10 100 1000 1 10 100 1000 Outdegree Outdegree Outdegree (a) Flickr (b) Wikipedia (c) YouTube-D Links Created (new links/node/day)PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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