Title: A limit theorem for an omnibus embedding of multiple random graphs
Abstract: 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. We describe 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. We prove 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. Experimental results demonstrate that the omnibus embedding improves upon existing methods, and in particular provides insight into analysis of real connectomic data.