Introduction - Graph Neural Architecture Search (GNAS) is an intriguing field that combines graph theory and neural network architecture search. There are various algorithms designed for GNAS, each with its own approach to discovering optimal graph neural network architectures. Objective - The main intention of the research is to determine a distinct search algorithm under GNAS which assists to identify the defined search space. The research examines the benefits and drawbacks of each search algorithm approach, gives thorough explanations of each strategy, and offers the required comparisons. Methodology - In order to effectively fulfil the study purpose and research questions, the article used non-experimental research under the quantitative research technique. The focus of the non-experimental study is on gathering pertinent information from big databases to improve our understanding of GNNs, GNAs, Search Algorithm and other recent advances in the field. Results - The study found that Graph-NAS has gained prominence as a research area because of its ability to get around certain challenges that occur with manually creating GNN models. The comparative study of the existing algorithm illustrates that every design has certain loopholes and challenges. Thus, further study is essential to explore the outcome of these algorithms from practical grounds.