This thesis investigates three problems in graph-structured modeling and learning. We first present a method for efficiently generating large instances from nonlinear preferential attachment models of network structure. This is followed by a description of diffusion-convolutional neural networks, a new model for graph-structured data which is able to outperform probabilistic relational models and kernel-on-graph methods at node classification tasks. We conclude with an optimal privacy-protection method for users of online services that remains effective when users have poor knowledge of an adversary's behavior.