Cervical cancer is a prevalent disease affecting the cervix cells in women and is one of the leading causes of mortality for women globally. The Pap smear test determines the risk of cervical cancer by detecting abnormal cervix cells. Early detection and diagnosis of this cancer can effectively increase the patient’s survival rate. The advent of artificial intelligence facilitates the development of automated computer-assisted cervical cancer diagnostic systems, which are widely used to enhance cancer screening. This study emphasizes the segmentation and classification of various cervical cancer cell types. An intuitive but effective segmentation technique is used to segment the nucleus and cytoplasm from histopathological cell images. Additionally, handcrafted features include different properties of the cells generated from the distinct cervical cytoplasm and nucleus area. Two feature rankings techniques are conducted to evaluate this study’s significant feature set. Feature analysis identifies the critical pathological properties of cervical cells and then divides them into 30, 40, and 50 sets of diagnostic features. Furthermore, a graph dataset is constructed using the strongest correlated features, prioritizes the relationship between the features, and a robust graph convolution network (GCN) is introduced to efficiently predict the cervical cell types. The proposed model obtains a sublime accuracy of 99.11% for the 40-feature set of the SipakMed dataset. This study outperforms the existing study, performing both segmentation and classification simultaneously, conducting an in-depth feature analysis, attaining maximum accuracy efficiently, and ensuring the interpretability of the proposed model. To validate the model’s outcome, we tested it on the Herlev dataset and highlighted its robustness by attaining an accuracy of 98.18%. The results of this proposed methodology demonstrate the dependability of this study effectively, detecting cervical cancer in its early stages and upholding the significance of the lives of women.