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132 of detecting a specific community partitioning. Second, if partial membership infor- mation about only one community is known, we look at the problem of detecting a specific community given a partial membership list. 7.3.1 Global community detection We assume that some fraction of the user population provides information about which communities they belong to. For example, some users on Facebook list their college and matriculation year in their profile. This information can be used to aid the automatic clustering algorithms. To evaluate whether this information can aid in identifying multiple community structures, we modified the Clauset [32] algorithm to take in attributes of a subset of the users. Instead of starting with every user in their own cluster, the algorithm pre- assigns users with the same attribute into the same cluster. We then run the algorithm as normal, effectively “seeding” it with the users who reveal their attributes. Finally, we calculate the modularity of the resulting partitioning, and then compare it to the partitioning based on the attributes of all users. To measure how similar these two community structures are, we use the normalized mutual information metric [53]. This metric is calculated as −2 xijlog(xijN ) i j xi.x.j xi.log(xi. ) + X.jlog(x.j ) (7.2) iNjN where x is a square matrix whose dimension is the number of communities detected. Each element xij represents the number of nodes in attribute-defined community iPDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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