Current graph-based analytic methods for single-cell RNA sequencing often utilizes gene-gene interaction networks. However, existing gene-gene interaction databases like STRING and BioGrid have significant drawbacks, including incompleteness, static nature, and lack of descriptive information. Recently, large language model (LLM) has demonstrated powerful capabilities in understanding and reasoning within the biomedical field without any fine-tuning. To address the drawbacks of traditional gene-gene interaction databases and use the reasoning capabilities of LLMs, we propose LLM-GeneGraph, a novel zero-shot generative framework that dynamically generates detailed, scientifically validated gene-gene interaction networks by integrating retrieval-augmented generation (RAG) techniques and employing an ensemble of three state-of-the-art LLMs along with an LLM-as-a-judge. The proposed method shows its capabilities to produce validated interactions and novel insights beyond the scope of traditional databases.