Evaluating Encodings for Bivariate Edges in Adjacency Matrices

2026-04-16

AI Summary

This study addresses the underexplored challenge of effectively visualizing bivariate distributions on graph edges under the spatial constraints of adjacency matrix layouts. The work proposes a novel approach that encodes edge-wise bivariate distributions using two statistical summaries: central tendency and dispersion. Through a preregistered crowdsourced experiment, the authors systematically evaluate four compact encoding designs—bivariate color mapping, embedded bar charts, and two superimposed mark types combining area or angle with color. Results demonstrate that the area-based superimposed marks and embedded bar charts yield the best overall performance, while angle-based encodings show moderate but inconsistent accuracy, and bivariate color mappings perform significantly worse. This research provides empirical evidence and practical guidance for designing visualizations of bivariate edge data in graph structures.

Technology Category

• Data Mining & Knowledge Management: Data Visualization & Summarization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Web data visualization
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

We present the first empirical evaluation of techniques for encoding distributions of quantitative edge values within adjacency matrices. In many real-world networks, edges represent not a single value but a set of measurements. While adjacency matrices preserve structural clarity, their compact cells limit the simultaneous display of multiple values. To address this, we explore edge encodings that represent distributions by two values: a measure of central tendency (mean, median, mode) and a measure of dispersion (standard deviation, variance, IQR). We select four possible encodings for evaluation that prior work has suggested are suitable for the limited space available in matrices: a bivariate color palette, embedded bar charts, and two overlaid-mark designs mapping the primary attribute to color and the secondary attribute to area or angle. In a preregistered crowdsourced study with 156 participants, we assessed performance of these encodings across eight analytical tasks and collected readability and aesthetic ratings. Results reveal clear performance regimes: area-based overlaid marks and bar charts achieved the highest overall performance; angle-based marks show moderate but less stable performance,and bivariate color consistently underperforms these alternatives. These findings clarify how visual channels behave under strict constraints and delineate the strengths and limitations of key design choices for multivariate edge visualization.

Problem

• bivariate edges
• adjacency matrices
• distribution encoding
• multivariate visualization
• visual encoding

Innovation

• bivariate edge encoding
• adjacency matrix visualization
• distribution representation
• empirical evaluation
• visual channels