In recent years, the use of graph theory in image analysis has gained traction, offering a flexible approach to handling complex data. This study explores the application of graph-based clustering techniques to embryo images captured during various developmental stages. We represent these images as graphs, where nodes correspond to enriched features extracted from image patches, and edges are established based on proximity and visual similarities. Dimensionality reduction was performed using Principal Component Analysis (PCA) and t-Distributed Stochastic Neighbor Embedding (t-SNE), followed by clustering using algorithms such as KMeans, Agglomerative Clustering, Gaussian Mixture Models (GMM), Spectral Clustering, and Birch. Our results indicate that GMM outperformed other methods, achieving the highest scores in metrics such as Adjusted Rand Index (0.1673), Normalized Mutual Information (0.2455), Homogeneity (0.2443), Completeness (0.2467), and V-Measure (0.2455), along with a strong Silhouette Score (0.4026). Notably, significant clustering tendencies were observed in the tB and tPN stages, while other stages exhibited a more mixed distribution, particularly in the tn and tSC stages. This research not only pioneers the use of graph-based methods in embryology but also suggests the potential for future improvements through the integration of advanced deep learning techniques and the expansion of data sets. The findings contribute significantly to the field of reproductive medicine, providing new tools for the analysis and classification of embryonic development stages.