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This chapter explores practical applications of network representation learning techniques for analyzing individual networks. It begins by addressing the community detection problem, demonstrating how to estimate community labels using network embeddings. The chapter then discusses the challenges posed by network sparsity and introduces efficient storage methods for sparse networks. The text proceeds to examine testing for differences between groups of edges, applying hypothesis testing to stochastic block models and structured independent edge models. It also covers model selection techniques for stochastic block models, helping readers choose appropriate levels of model complexity. The chapter introduces the vertex nomination problem, which aims to identify nodes similar to a set of known "seed" nodes. It presents spectral vertex nomination techniques and explores extensions to related problems. Finally, the chapter addresses out-of-sample embedding, providing efficient strategies for embedding new nodes into existing network representations. This approach is particularly valuable for large-scale, dynamic networks where frequent re-embedding would be computationally prohibitive.
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