Network Global Testing by Counting Graphlets
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Proceedings of the 35th International Conference on Machine Learning, PMLR 80:23332341, 2018.
Abstract
Consider a large social network with possibly severe degree heterogeneity and mixedmemberships. We are interested in testing whether the network has only one community or there are more than one communities. The problem is known to be nontrivial, partially due to the presence of severe degree heterogeneity. We construct a class of test statistics using the numbers of short paths and short cycles, and the key to our approach is a general framework for canceling the effects of degree heterogeneity. The tests compare favorably with existing methods. We support our methods with careful analysis and numerical study with simulated data and a real data example.
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