Proximity Alert: Ipelets for Neighborhood Graphs and Clustering

2026-03-27

AI Summary

Existing tools struggle to intuitively illustrate the structure and behavior of neighborhood graphs and clustering algorithms. This work proposes a suite of Lua-based Ipe plugins (Ipelets) that, for the first time, systematically integrates interactive visualizations of over ten neighborhood graphs—such as ε-neighborhood graphs, k-nearest neighbor graphs, and Gabriel graphs—with prominent clustering algorithms including DBSCAN, HDBSCAN, and k-means within the unified and extensible Ipe vector graphics editing platform. By offering an open-source, cohesive environment for visual exploration, this toolkit substantially enhances comprehension of algorithmic mechanisms and significantly improves efficiency in both teaching and research, thereby addressing a critical gap in the availability of effective, integrated visual analytics tools for this domain.

Abstract

Neighborhood graphs and clustering algorithms are fundamental structures in both computational geometry and data analysis. Visualizing them can help build insight into their behavior and properties. The Ipe extensible drawing editor, developed by Otfried Cheong, is a widely used software system for generating figures. One particular aspect of Ipe is the ability to add Ipelets, which extend its functionality. Here we showcase a set of Ipelets designed to help visualize neighborhood graphs and clustering algorithms. These include: $\eps$-neighbor graphs, furthest-neighbor graphs, Gabriel graphs, $k$-nearest neighbor graphs, $k^{th}$-nearest neighbor graphs, $k$-mutual neighbor graphs, $k^{th}$-mutual neighbor graphs, asymmetric $k$-nearest neighbor graphs, asymmetric $k^{th}$-nearest neighbor graphs, relative-neighbor graphs, sphere-of-influence graphs, Urquhart graphs, Yao graphs, and clustering algorithms including complete-linkage, DBSCAN, HDBSCAN, $k$-means, $k$-means++, $k$-medoids, mean shift, and single-linkage. Our Ipelets are all programmed in Lua and are freely available.

Problem

• neighborhood graphs
• clustering algorithms
• visualization
• computational geometry
• data analysis

Innovation

• Ipelets
• neighborhood graphs
• clustering visualization
• computational geometry
• Lua scripting