Unsupervised term discovery (UTD) is the task of automatically identifying the repeated words and phrases in a collection of speech audio without relying on any language-specific resources. While the solution space for the task is far from fully explored, the dominant approach to date decomposes the discovery problem into two steps, where (i) segmental dynamic time warping is used to search the speech audio for repeated acoustic patterns, and (ii) these individual repetitions are partitioned into word/phrase categories using graph clustering. In this paper, we perform an unprecedented evaluation of a wide range of advanced graph clustering methods for the UTD task. We conduct our study in the evaluation framework of the Zero Resource Speech Challenge. We find that, for a range of features and languages, modularity-based clustering improves UTD performance most consistently, often by a wide margin. When paired with out-of-language deep neural net bottleneck features, we find performance near that of a high-resource UTD system.