In areas of digital image processing and computer vision, image segmentation is defined as a crucial process that divides an image into many segments for more straightforward and accurate object analysis. Making use of graph-based techniques as an effective tool for segmenting images has drawn more consideration recently. Since graph-based techniques are attractive and increasingly prevalent and can designate image properties, in this article, some of the primary graph-based techniques have been presented. This scheme utilizes graph theory to create a graph depiction of an image in which each pixel is represented as a node and the edges show the degree of similarity between two pixels. When items are represented by vertices and an edge connects them, a graph may be used to depict the relationship between them. To divide a graph into sub-graphs that reflect significant items of interest, this study explores some graph theoretical approaches for image segmentation, including minimum spanning tree, pyramid-based, graph cut-based, and interactive image segmentation and their employing in significant image processing fields such as medical image analysis for infection diagnosis, and remote sensing.