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7.2.1 Friends with common attributes Our first observation is that users are statistically much more likely to be friends with other users who share their attributes. In order to show this, we calculated for each attribute a (such as college or matriculation year) Sa=|{(i,j)∈E: s.t.ai=aj}| (7.1) |E| where ai represents the value of attribute a for user i, and E represents the set of all links. Sa therefore represents the fraction of links for which users share the same value of attribute a. Finally, we divided this by what would be expected in a graph with a similar distribution of attributes but with the links placed randomly between users. The resulting value, which we call affinity, ranges from 0 to ∞ and represents the ratio of the fraction of links between attribute-sharing users, relative to what would be expected in a random graph. Thus, an affinity greater than 1 indicates that links are positively correlated with user attributes. Table 7.1 shows the affinity of the various attributes for the undergraduates and graduate students at Rice. We observe that for all attributes, a significant affinity is observed, showing that links in the Rice network are correlated with attributes. It is interesting to note that certain attributes are stronger than others: for example, grad- uate students have a much strong affinity for other students in the same department when compared to other students in the same matriculation year. In some cases, the affinity is as high as 10, implying that users connected by a link are 10 times more likely to share an attribute that would be expected in a random graph. In summary, 126PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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