An essential step in data mining and machine learning is feature selection, which aims to enhance model performance by lowering dimensionality while maintaining pertinent information. The capability of graph-based feature selection to represent intricate relationships between features has drawn a lot of interest. This survey categorizes existing graph-based feature selection techniques into four major categories: Graph Similarity and Distance-Based Feature Selection, Graph Centrality and Ranking-Based Feature Selection, Graph Clustering and Structure-Based Feature Selection, and Hybrid and Optimization-Driven Graph Feature Selection. Furthermore, the survey identifies important trends, benefits, and challenges associated with graph-based feature selection by systematically examining and contrasting the approaches used in each category. It also identifies potential research directions, emphasizing the need for adaptive and scalable solutions to enhance feature selection performance across diverse applications.