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138 by Luo [99], we use a greedy approach to maximize the normalized conductance. We initially divide the graph into two components A and B, with A = S initially. At each step, we select a user v ∈ V in B that upon adding v to A yields the highest increase in the normalized conductance C for A. We repeat this process, adding users to A, until no remaining user would produce an increase in the normalized conductance C for A. At this point, we stop and return the community A as the result. The primary difference between our method and the previous approaches is the use of a metric that is weighted against a random graph. We found that the metrics used by previous approaches are all biased towards large communities. For example, the metric used by Luo et al. [99] is based on the ratio between the number of intra-community links to the number of inter-community links. As a community grows larger, this value naturally increases; in fact, it becomes infinite if an entire connected component is viewed as a community. Thus, these approaches often have trouble detecting large communities in the network, as they often proceed to detect the entire graph as a community. By weighting our metric against a random graph, we can detect both the small-scale and large-scale communities that exist. Evaluation To see how well our algorithm and others perform, we evaluate the performance along two axes. Assume that each algorithm takes as input a subset S of users with attribute H, and the social network graph. The algorithm then returns a set of usersPDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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