This paper explores the use of graph-theoretical methods, specifically minimal spanning trees (MST), to detect and describe cluster structures in point sets. The author, C. T. Zahn, draws inspiration from human perception of gestalts or point-groupings, aiming to develop algorithms that can identify and interpret clusters in both two-dimensional and higher-dimensional spaces. The paper covers various applications of cluster detection, including taxonomy, pattern recognition, and particle track description. Key concepts such as proximity, similarity, and the principles of gestalt psychology are discussed, providing a theoretical foundation for the methods. The author introduces intuitive methods for cluster detection and then advances to more sophisticated techniques, including the use of MSTs. The paper includes detailed analyses of several planar cluster detection problems and demonstrates the effectiveness of MSTs in describing cluster shapes and topologies. The author also discusses the advantages of MSTs, such as determinacy, easy interpretation, and invariance under monotone transformations. Finally, the paper explores the application of cluster detection in taxonomy and the selection of feature spaces for pattern recognition, highlighting the importance of good feature spaces in achieving accurate discrimination.This paper explores the use of graph-theoretical methods, specifically minimal spanning trees (MST), to detect and describe cluster structures in point sets. The author, C. T. Zahn, draws inspiration from human perception of gestalts or point-groupings, aiming to develop algorithms that can identify and interpret clusters in both two-dimensional and higher-dimensional spaces. The paper covers various applications of cluster detection, including taxonomy, pattern recognition, and particle track description. Key concepts such as proximity, similarity, and the principles of gestalt psychology are discussed, providing a theoretical foundation for the methods. The author introduces intuitive methods for cluster detection and then advances to more sophisticated techniques, including the use of MSTs. The paper includes detailed analyses of several planar cluster detection problems and demonstrates the effectiveness of MSTs in describing cluster shapes and topologies. The author also discusses the advantages of MSTs, such as determinacy, easy interpretation, and invariance under monotone transformations. Finally, the paper explores the application of cluster detection in taxonomy and the selection of feature spaces for pattern recognition, highlighting the importance of good feature spaces in achieving accurate discrimination.