In the wake of the accelerated advancements in computing technology and the onset of the big data era, image segmentation technology has emerged as a pivotal component within the domain of medical image analysis. The primary objective of image segmentation is to partition an image into constituent regions characterized by distinct features, thereby facilitating precise quantitative analysis crucial for disease diagnosis, biomarker discovery, and broader medical research endeavours. Among various techniques, the graph theoretical approach (GTA) stands out due to its robust theoretical underpinnings. This approach not only structures image elements into coherent mathematical frameworks but also enhances problem formulation, rendering it more adaptable and computationally efficient. This paper provides a comprehensive overview of essential graph theoretical approaches (GTAs), such as minimum spanning tree algorithms, graph cuts, Markov random fields, and shortest path approaches, and their application in biomedical imaging, including MRI images, CT scans and Ultrasound images. It discusses the challenges of high computational demands, scalability for large image datasets, and integrating deep learning. Despite these challenges, the paper highlights the exceptional analytical power of GTAs in processing complex biomedical images.