Directly motivated by security-related applications from the Homeland Security Enterprise, we focus on the privacy-preserving analysis of graph data, which provides the crucial capacity to represent rich attributes and relationships. In particular, we discuss two directions, namely privacy-preserving graph generation and federated graph learning, which can jointly enable the collaboration among multiple parties each possessing private graph data. For each direction, we identify both "quick wins" and "hard problems". Towards the end, we demonstrate a user interface that can facilitate model explanation, interpretation, and visualization. We believe that the techniques developed in these directions will significantly enhance the capabilities of the Homeland Security Enterprise to tackle and mitigate the various security risks.