Goal: The presence of microcalcification clusters is a primary sign of breast cancer; however, it is difficult and time consuming for radiologists to classify microcalcifications as malignant or benign. In this paper, a novel method for the classification of microcalcification clusters in mammograms is proposed. Methods: The topology/connectivity of individual microcalcifications is analysed within a cluster using multiscale morphology. This is distinct from existing approaches that tend to concentrate on the morphology of individual microcalcifications and/or global (statistical) cluster features. A set of microcalcification graphs are generated to represent the topological structure of microcalcification clusters at different scales. Subsequently, graph theoretical features are extracted which constitute the topological feature space for modelling and classifying microcalcification clusters. k-Nearest Neighbours based classifiers are employed for classifying microcalcification clusters. Results:The validity of the proposed method is evaluated using two well-known digitised datasets (MIAS and DDSM) and a full-field digital dataset. High classification accuracies (up to 96%) and good ROC results (area under the ROC curve up to 0.96) are achieved. A full comparison with related publications is provided, which includes a direct comparison. Conclusion: The results indicate that the proposed approach is able to outperform the current state-of-the-art methods. Significance: This work shows that topology modelling is an important tool for microcalcification analysis not only because of the improved classification accuracy but also because the topological measures can be linked to clinical understanding.