Graphs are fast emerging as a common data structure used in many scientific and engineering fields. While a wide variety of techniques exist to analyze graph datasets, practitioners currently lack a signal processing theory akin to that of detection and estimation in the classical setting of vector spaces with Gaussian noise. Using practical detection examples involving large, random "background" graphs and noisy real-world datasets, the authors present a novel graph analytics framework that allows for uncued analysis of very large datasets. This framework combines traditional computer science techniques with signal processing in the context of graph data, creating a new research area at the intersection of the two fields.