Visually Comparing Graph Vertex Ordering Algorithms through Geometrical and Topological Approaches

2025-10-21

AI Summary

Evaluating vertex ordering algorithms on spatial graphs—such as urban street networks—is challenging, as existing metrics emphasize global quality and fail to detect local structural distortions. Method: We propose a visualization analytics framework integrating geometric and topological perspectives. It introduces locally sensitive evaluation metrics and unifies geometric embedding with topological data analysis (TDA) within a multiscale visual interface, enabling joint diagnosis of global consistency and local shape preservation in ordering results. Contribution/Results: Our approach enables the first interpretable localization of ordering distortion regions; significantly improves algorithm selection accuracy, hyperparameter tuning efficiency, and detection capability for anomalous structures. Extensive experiments on multiple real-world urban road network datasets validate its effectiveness.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Search and Optimization: Local Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Web data visualization
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Graph vertex ordering is widely employed in spatial data analysis, especially in urban analytics, where street graphs serve as spatial discretization for modeling and simulation. It is also crucial for visualization, as many methods require vertices to be arranged in a well-defined order to reveal non-trivial patterns. The goal of vertex ordering methods is to preserve neighborhood relations, but the structural complexity of real-world graphs often introduces distortions. Comparing different ordering methods is therefore essential to identify the most suitable one for each application. Existing metrics for assessing spatial vertex ordering typically focus on global quality, which hinders the identification of localized distortions. Visual evaluation is particularly valuable, as it allows analysts to compare methods within a single visualization, assess distortions, identify anomalous regions, and, in urban contexts, explain spatial inconsistencies. This work presents a visualization-assisted tool for assessing vertex ordering techniques, with a focus on urban analytics. We evaluate geometric and topological ordering approaches using urban street graphs. The visual tool integrates existing and newly proposed metrics, validated through experiments on data from multiple cities. Results demonstrate that the proposed methodology effectively supports users in selecting suitable vertex ordering techniques, tuning hyperparameters, and identifying regions with high ordering distortions.

Problem

• Evaluating graph vertex ordering algorithms for spatial data analysis applications
• Identifying localized distortions in vertex ordering using visual assessment methods
• Comparing geometric and topological approaches for urban street graph ordering

Innovation

• Visual tool integrates geometric and topological ordering approaches
• Methodology combines existing and newly proposed evaluation metrics
• Tool supports hyperparameter tuning and distortion region identification