We investigate how to address the shortcomings of the popular One-Class Collaborative Filtering (OCCF) methods in handling challenging “sparse” dataset in one-class setting (e.g., clicked or bookmarked), and propose a novel graph-theoretic OCCF approach, named as gOCCF, by exploiting both positive preferences (derived from rated items) as well as negative preferences (derived from unrated items). In capturing both positive and negative preferences as a bipartite graph, further, we apply the graph shattering theory to determine the right amount of negative preferences to use. Then, we develop a suite of novel graph-based OCCF methods based on the random walk with restart and belief propagation methods. Through extensive experiments using 3 real-life datasets, we show that our gOCCF effectively addresses the sparsity challenge and significantly outperforms all of 8 competing methods in accuracy on very sparse datasets while providing comparable accuracy to the best performing OCCF methods on less sparse datasets. The datasets and implementations used in the empirical validation are available for access: https://goo.gl/sfiawn.