Graphs are effective data structures for modeling relationships in data. As interest in graphs increases with the development of graph neural networks, various works have been conducted to study fundamental problems of machine learning in the graph domain. This talk introduces our recent works for positive-unlabeled (PU) learning and data augmentation on graphs. The first part introduces our work (ICDM-21) for solving PU learning on graphs by modeling real-world graphs as Markov networks with an EM formulation. The second part introduces our work (WWW-22) for designing model-agnostic algorithms that augment the structure of real-world graphs while minimizing changes in semantic information.