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133 that appeared in the detected community j. x.i and xi. denotes sum over column i, and sum over row i respectively, and N is the number of nodes in the graph. At a high level, the metric ranges between 0 and 1, with 0 representing no correlation between the two community structures, and 1 representing a perfect match. 1 0.8 0.6 0.4 0.2 0 Figure 7.1 : Normalized mutual information versus the fraction of users who reveal their community for Rice undergraduates. Revealing more information naturally leads to partitionings with higher correlations, especially for the college and year attributes. This result shows that different attributes can be accurately inferred with as few as 20% of users revealing their attributes. Figure 7.1 plots the results of this experiment for the undergraduates, by showing the normalized mutual information for each attribute. Separate lines are plotted for each attribute, and the correlation value is with respect to the attribute that users are revealing. Two trends can be seen in this graph. First, we observe that both college and year quickly lead to community structures with significant correlation. In fact, when just 20% of users reveal their college or year, we can infer the attributes for the remaining users with over 80% accuracy. Second, this is not the case for major of study. However, this result is not surprising, as we observed in the previous section College Year Major 0 0.10.20.30.40.50.60.70.80.9 1 Fraction of Users Revealed Normalized Mutual InformationPDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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