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139 R, representing the other members it believes also have attribute H, based on the community structure in the network. We define the recall to be |R∩H| (7.5) representing the fraction of the remaining community members that the algorithm returns. Similarly, we define the precision to be |R∩H| (7.6) |H \ S| |R| representing the fraction of the returned users who are actually in the community. Thus, an ideal algorithm would have a recall of 1 (returning all of the remaining users) as well as a precision of 1 (only returning users who are actually in the community). We now evaluate our algorithm on the Rice data set along with the algorithms of Luo [99], Bagrow [13], and Clauset [31]. First, we examine how well they perform on the undergraduate population by providing the algorithms with varying-size subsets of the students with common attributes such as college, matriculation year, and major. For each attribute (i.e., each college, each major), we select 20 random subsets of users of each size. We then evaluate how well the algorithms perform when given each of these random subsets as input. For fair comparison with the other algorithms, a few parameters and modifica- tions were required. First, none of the other algorithms accept as input a set of seed nodes; we naturally extended them to start with a set of nodes rather than a single node. Second, the algorithm proposed by Clauset does not specify a stopping con- dition; instead, it requires the user to specify the number of nodes to be added toPDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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