Representing and analyzing structural differences among graphs help gain insight into the difference related patterns such as dynamic evolutions of graphs. Conventional solutions leverage representation learning techniques to encode structural information, but lack an intuitive way of studying structural semantics of graphs. In this article, we propose a representation-and-analysis scheme for structural differences among graphs. We propose a deep-learning-based embedding technique to encode multiple graphs while preserving semantics of structural differences. We design and implement a web-based visual analytics system to support comparative study of features learned from the embeddings. One distinctive feature of our approach is that it supports semantics-aware construction, quantification, and investigation of latent relations encoded in graphs. We validate the usability and effectiveness of our approach through case studies with three datasets.