The search for biomarkers of diseases has traditionally involved analyzing disease data as a whole. But this approach has largely ignored the significance of disease progression at different stages. Acknowledging the fact that different genes may be responsible for disease progression in different stages, we have developed a novel approach to analyse the temporal graphs that employs a modified version of betweenness centrality, known as ''transition centrality''. Applying this measure to the stage-wise data of three common diseases, namely Alzheimer's disease, Parkinson's disease, and Human breast cancer, we identified successfully a set of genes that may be key players in disease progression. The findings reveal that stage-specific genes can be identified using transition centrality as the specificity of these genes in a particular stage was validated through an extensive review of the relevant literature. Remarkably, this analysis yielded a number of promising disease-related genes for each of the diseases that have been studied, such as RARA and NOS1 in Alzheimer's disease, LRRK2 in Parkinson's disease, and BRCA1, ACTB, TYMS, and many others in human breast cancer. Our results demonstrate that the transition centrality analysis can be utilized to identify stage-specific genes of diseases.