Graphs are a powerful way to model interactions and relationships in data from a wide variety of application domains. In this setting, entities represented by vertices at the \"Center\" of the graph are often more important than those associated with vertices on the \"Fringes\". For example, central nodes tend to be more critical in the spread of information or disease and play an important role in clustering/community formation. Identifying such \"Core\" vertices has recently received additional attention in the context of network experiments, which analyze the response when a random subset of vertices is exposed to a treatment (e.g. inoculation, free product samples, etc).