In this paper, we propose new image forgery detection and localization algorithms by recasting these problems as graph-based community detection problems. We define localized image tampering as any locally applied manipulation, including splicing and airbrushing, but not globally applied processes such as compression, whole-image resizing or contrast enhancement, etc. To show this, we propose an abstract, graph-based representation of an image, which we call the Forensic Similarity Graph. In this representation, small image patches are represented by graph vertices, and edges that connect pairs of vertices are assigned according to the forensic similarity between patches. Localized tampering introduces unique structure into this graph, which align with a concept called "communities" in graph-theory literature. A community is a subset of vertices that contain densely connected edges within the community, and relatively sparse edges to other communities. In the Forensic Similarity Graph, communities correspond to the tampered and unaltered regions in the image. As a result, forgery detection is performed by identifying whether multiple communities exist, and forgery localization is performed by partitioning these communities. In this paper, we additionally propose two community detection techniques, adapted from literature, to detect and localize image forgeries. We experimentally show that our proposed community detection methods outperform existing state-of-the-art forgery detection and localization methods.