This paper provides a comprehensive review of graph-based image segmentation methods. Various graph-based algorithms and their applications are explored, including multiple surface segmentation, saliency detection, and colour-texture segmentation. This work introduced a superpixel algorithm and Simple Linear Iterative Clustering (SLIC) algorithm to segment an image using a graph representation. The results show that graph-based methods like SLIC can effectively model images as graphs and optimize segmentation to group visually coherent pixels while respecting intensity variations and spatial proximity between pixels. The key concepts, importance of image segmentation, and challenges are also discussed. While the demonstration provides basic validation of graph-based principles, opportunities remain for improvement such as incorporating edge features and neural networks to address oversegmentation issues. Overall, the review and experimental results highlight the effectiveness of graph-based segmentation methods in computer vision domains.