Graphs are ubiquitous, which makes machine learning on graphs an important research area. While there are many aspects to this field, our research is focused primarily on two aspects of it. The first research question concerns privacy in graphs, where our work primarily focuses on preserving structural privacy in graphs. The second research question is about generating graphs. With applications in various fields such as drug discovery, designing novel proteins, etc., graph generation is emerging as an essential problem. This paper briefly describes the problems and the methodology to address them.