In the current digital era, community detection in social network graphs is a critical task for understanding group behavior, influence patterns, and information flow. While traditional approaches primarily leverage graph topology, recent advances in Large Language Models (LLMs) offer new opportunities to incorporate semantic and contextual signals into this process. In this paper, we conduct a comprehensive study to evaluate how different LLM-based techniques perform in detecting communities across social graphs. We propose 3-step method namely GraphMinds which is based on GPT-4o model and prompt-based inference to integrate LLM outputs with structural features. Using 6 real-world social network datasets, we benchmark these methods across key metrics such as Normalized Mutual Information (NMI), Adjusted Rand Index (ARI), Variation of Information (VOI) and cluster purity. Our findings reveal that LLMs can be used for community detection for small sized graphs when combined with graph-aware strategies, and that specific configurations—such as instruction-tuned models or prompt engineering—yield substantial gains. This work provides insights into the strengths and limitations of applying language models to structured social data, offering guidance for future research in LLM-driven graph analysis.