Graph-theoretical methods for detecting and describing Gestalt clusters are presented. These methods, based on minimal spanning trees (MSTs), are capable of identifying various cluster structures in arbitrary point sets. The approach is motivated by the human perception of Gestalt clusters, where proximity is a key principle. The methods are applicable to two-dimensional and higher-dimensional spaces, as well as general metric spaces. Advantages include determinacy, ease of interpretation, conformity to Gestalt principles, and invariance under monotonic transformations of interpoint distance. The methods are applied to taxonomy, pattern recognition, and other areas. Examples include cluster detection in biological data, pattern recognition, and particle track analysis. The MST is shown to be a powerful tool for cluster detection and description, with the ability to identify clusters and their boundaries. Theoretical results support the effectiveness of MSTs in cluster analysis, and computational experience demonstrates their utility. The methods are also applicable to touching clusters, Gaussian clusters, and density gradient detection. The rationale for using MSTs as cluster descriptions is based on their ability to capture the structure of point sets and their invariance under certain transformations. The methods are generalizable to higher-dimensional spaces and have been tested on various data sets. The paper concludes with directions for further research and references to related work.Graph-theoretical methods for detecting and describing Gestalt clusters are presented. These methods, based on minimal spanning trees (MSTs), are capable of identifying various cluster structures in arbitrary point sets. The approach is motivated by the human perception of Gestalt clusters, where proximity is a key principle. The methods are applicable to two-dimensional and higher-dimensional spaces, as well as general metric spaces. Advantages include determinacy, ease of interpretation, conformity to Gestalt principles, and invariance under monotonic transformations of interpoint distance. The methods are applied to taxonomy, pattern recognition, and other areas. Examples include cluster detection in biological data, pattern recognition, and particle track analysis. The MST is shown to be a powerful tool for cluster detection and description, with the ability to identify clusters and their boundaries. Theoretical results support the effectiveness of MSTs in cluster analysis, and computational experience demonstrates their utility. The methods are also applicable to touching clusters, Gaussian clusters, and density gradient detection. The rationale for using MSTs as cluster descriptions is based on their ability to capture the structure of point sets and their invariance under certain transformations. The methods are generalizable to higher-dimensional spaces and have been tested on various data sets. The paper concludes with directions for further research and references to related work.