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The problem of detecting a small, anomalous subgraph within a large background network is important and applicable to many fields. The non-Euclidean nature of graph data, however, complicates the application of classical detection theory in this context. A recent statistical framework for anomalous subgraph detection uses spectral properties of a graph's modularity matrix to determine the presence of an anomaly. In this paper, this detection framework and the related algorithms are applied to data focused on a specific application: detection of a threat subgraph embedded in a social network. The results presented use data created to simulate threat activity among noisy interactions. The detectability of the threat subgraph and its separability from the noise is analyzed under a variety of background conditions in both static and dynamic scenarios.