“…Graphs are an increasingly popular data modality in scientific research and statistical inference, with diverse applications in connectomics [6], social network analysis [7], and pattern recognition [21], to name a few. Many joint graph inference methodologies (see, for example, [45,18,6,37]), joint graph embedding algorithms (see, for example, [19,34,41,39]) and graph-valued time-series methodologies (see, for example, [23,33,46,50]) operate under the implicit assumption that an explicit vertex correspondence is a priori known across the vertex sets of the graphs. While this assumption is natural in a host of real data settings, in many applications these correspondences may be unobserved and/or errorfully observed [48].…”