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7.3.2 Local community detection We now look at detecting communities on a local scale. This is different from the problem in the previous section, where we assumed that partial information about all users in the network is known. Instead, for example, we may know that a subset of five users all live in the same dormitory, and we wish to determine the other users (for which we do not have any information) who also live in that dormitory. To detect these communities, we extend the previously proposed approaches for local community detection to take a seed set of nodes. While exploring local community detection, we found that previous approaches performed well when detecting certain attributes, but did not perform well on others. For example, we found that the algorithm of Luo [99] could infer the members of a res- idential college at Rice, but was not able to infer the members of larger communities, such as all students in the same matriculation year. Thus, we propose a new method for detecting a single community, based on the metric of normalized conductance. We first describe this new metric below, followed by a description of our algorithm, and finally evaluate the algorithms on our Rice data set. Normalized conductance We first define a metric that rates the quality of a single community (as opposed to modularity, which rates the community structure of a partitioning of a graph into a collection of communities). To provide a measure for the quality of a community, 135PDF Image | Online Social Networks: Measurement, Analysis, and Applications to Distributed Information Systems
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