Several types of breast carcinomas tend to spread along the surface of the ductal lumen. Spontaneous nipple discharge can be an early symptom of such cancer development that does not otherwise result in visible mammographic changes. An imaging procedure that can visualize such symptoms is galactography. We focus on characterizing the topology of the ductal network in galactograms based on fractal properties. Statistically significant differences of fractal properties were detected among healthy subjects and patients with reported galactographic findings. We performed receiver operating characteristic (ROC) curve analysis in order to assess the accuracy of using the regularization dimension values for separating among ductal trees. The area under the ROC curve observed was 0.86.