Local spatial arrangement of nuclei in histopathology images of different cancer subtypes has been shown to have prognostic value. In order to capture localized nuclear architectural information, local cell cluster graph-based measurements have been proposed. However, conventional ways of cell graph construction only utilize nuclear spatial proximity, and do not differentiate between different cell types while constructing the graph. In this paper, we present feature-driven local cell cluster graph (FLocK), a new approach to constructing local cell graphs by simultaneously considering spatial proximity and attributes of the individual nuclei (e.g. shape, size, texture). In addition, we have designed a new set of quantitative graph-derived metrics to be extracted from FLocKs, in turn capturing the interplay between different proximally located clusters of nuclei. We have evaluated the efficacy of FLocK features extracted from H&E stained tissue images in two clinical applications: to classify short-term vs. long-term survival among patients of early stage non-small cell lung cancer (ES-NSCLC), and also to predict human papillomavirus (HPV) status of oropharyngeal squamous cell carcinoma (OP-SCCs). In the classification of long-term vs. short-term survival among patients of ES-NSCLC (training cohort, n = 434), the top 10 discriminative FLocK features related to the variation of FLocK size and intersected FLocK distance were identified, via Minimum Redundancy and Maximum Relevance (MRMR) selection, in 100 runs of 10-fold cross-validation, and in conjunction with a linear discriminant classifier yielded a mean AUC of 0.68 for predicting survival in the training cohort. This is better than other state-of-art histomorphometric and deep learning classifiers (cell cluster graphs (AUC = 0.62), global cell graph (AUC = 0.56), nuclear shape (AUC = 0.54), nuclear orientation (AUC = 0.61), AlexNet (AUC = 0.55), ResNet (AUC = 0.56)). The FLocK-based classifier yielded an AUC of 0.70 in an independent testing cohort (n = 150). The patients identified as "high-risk" had significantly poorer overall survival in the testing cohort, with a hazard ratio (95% confidence interval) of 2.24 (1.24-4.05), p = 0.01144). In the classification of HPV status of OP-SCC, the top three FLocK features pertaining to the portion of intersected FLocKs were used to construct a classifier, which yielded an AUC of 0.80 in the training cohort (n = 50), and an accuracy of 0.78 in an independent testing cohort (n = 35). The combination of FLocK measurements with cell cluster graphs, nuclear orientation, and nuclear shape improved the training AUC to 0.87, 0.91 and 0.85, respectively. Deep learning approaches yielded marginally better performance than the FLocK-based classifier in this application, with AUC = 0.78 for AlexNet, AUC = 0.81 for ResNet, and AUC = 0.76 for FLocK-based classifier in the testing cohort. However, the combination of two hand-crafted features: FLocK and nuclear orientation yielded a better performance (AUC = 0.84). FLocK provides a unique and quantitative way to analyze histology images of solid tumors and interrogate tumor morphology from a different aspect than existing histomorphometrics. The source code can be accessed at https://github.com/hacylu/FLocK.