Performing statistical inference on collections of graphs is of import to many disciplines. Graph embedding, in which the vertices of a graph are mapped to vectors in a low-dimensional Euclidean space, has gained traction as a basic tool for graph analysis. In this talk, I will present an omnibus embedding in which multiple graphs on the same vertex set are jointly embedded into a single space with a distinct representation for each graph. I will show a central limit theorem for this omnibus embedding, and show that this simultaneous embedding into a common space allows comparison of graphs without the need to perform pairwise alignments of graph embeddings. I will present experimental results demonstrating that the omnibus embedding improves upon existing methods, allowing better power in multiple-graph hypothesis testing and yielding better estimation in a latent position model. If time allows, I will discuss preliminary work applying the omnibus embedding to brain imaging data.