Features extracted from cell networks have become popular tools in histological image analysis. However, existing features do not take sufficient advantage of the cycle structure present within the cell networks. We introduce a new class of network cycle features that take advantage of such structures. We demonstrate the utility of these features for automated prostate cancer scoring using histological images. Prostate cancer is commonly scored by pathologists using the Gleason grading system and our automated system based upon network cycle features serves an important need in making this process less labor-intensive and more reproducible. Our system first extracts the cells from the histological images, computes networks from the cell locations and then computes features based upon statistics for the different cycles present in these networks. Using an SVM (Support Vector Machine) classifier on these features, we demonstrate the efficacy of our system in distinguishing between grade 3 and grade 4 prostate tumors. We also show the superiority of our approach over previously developed systems for this problem based upon texture features, fractal features and alternative network features.