Obtaining the right resume for screening becomes a very crucial point in recruitment. The process must weigh in facing massive volume, fairness, and deliver results in due time. Weighing each resume manually takes time and might be biased and inconsistent across recruiters. The paper presents IntelliHire, an intelligent resume screening system that uses a hybrid approach combining GNNs and Transformer-based language models for better accuracy, interpretability, and fairness. A novel dataset, Graph Res-HR, containing 3,000 resumes and 600 job descriptions in five domains–Software Engineering, Data Science, Marketing, Finance, and UX Design–with structured annotation of skills, education, and experience, and human-rated relevance scores is created. The core of IntelliHire encodes textual information extracted from resumes and job descriptions using a fine-tuned transformer model, builds a relational graph linking candidates, skills, education, and job requirements, and applies GNNs to capture cross-entity interactions. A ranking module then computes relevance scores by aggregating the textual and graph embeddings. To finish, experimental results show that IntelliHire outperforms traditional machine learning and transformer-only models with regard to accuracy, Mean Average Precision (MAP), nDCG, and AUC-ROC and also offers interpretability for the recruiters. The system proposed is, therefore, a strong, transparent, and fair method of resume screening that can take care of some of the problems faced by present recruiting avenues.