The structure of protein-protein interaction (PPI) networks has already been successfully used as a source of new biological information. Even though cardiovascular diseases (CVDs) are a major global cause of death, many CVD genes still await discovery. We explore ways to utilize the structure of the human PPI network to find important genes for CVDs that should be targeted by drugs. The hope is to use the properties of such important genes to predict new ones, which would in turn improve a choice of therapy. We propose a methodology that examines the PPI network wiring around genes involved in CVDs. We use the methodology to identify a subset of CVD-related genes that are statistically significantly enriched in drug targets and "driver genes." We seek such genes, since driver genes have been proposed to drive onset and progression of a disease. Our identified subset of CVD genes has a large overlap with the Core Diseasome, which has been postulated to be the key to disease formation and hence should be the primary object of therapeutic intervention. This indicates that our methodology identifies "key" genes responsible for CVDs. Thus, we use it to predict new CVD genes and we validate over 70% of our predictions in the literature. Finally, we show that our predicted genes are functionally similar to currently known CVD drug targets, which confirms a potential utility of our methodology towards improving therapy for CVDs.