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Extending adjacency matrices to 3D with triangles

Rusheng Pan, Helen C. Purchase, Tim Dwyer, Wei Chen

TL;DR

A 3D matrix reordering technique is designed and an immersive interactive system is implemented to assist in visualizing and analyzing closed triads in social networks and shows substantial added value over node-link diagrams in improving the efficiency and accuracy of manipulating and understanding the social network triads.

Abstract

Social networks are the fabric of society and the subject of frequent visual analysis. Closed triads represent triangular relationships between three people in a social network and are significant for understanding inherent interconnections and influence within the network. The most common methods for representing social networks (node-link diagrams and adjacency matrices) are not optimal for understanding triangles. We propose extending the adjacency matrix form to 3D for better visualization of network triads. We design a 3D matrix reordering technique and implement an immersive interactive system to assist in visualizing and analyzing closed triads in social networks. A user study and usage scenarios demonstrate that our method provides substantial added value over node-link diagrams in improving the efficiency and accuracy of manipulating and understanding the social network triads.

Extending adjacency matrices to 3D with triangles

TL;DR

A 3D matrix reordering technique is designed and an immersive interactive system is implemented to assist in visualizing and analyzing closed triads in social networks and shows substantial added value over node-link diagrams in improving the efficiency and accuracy of manipulating and understanding the social network triads.

Abstract

Social networks are the fabric of society and the subject of frequent visual analysis. Closed triads represent triangular relationships between three people in a social network and are significant for understanding inherent interconnections and influence within the network. The most common methods for representing social networks (node-link diagrams and adjacency matrices) are not optimal for understanding triangles. We propose extending the adjacency matrix form to 3D for better visualization of network triads. We design a 3D matrix reordering technique and implement an immersive interactive system to assist in visualizing and analyzing closed triads in social networks. A user study and usage scenarios demonstrate that our method provides substantial added value over node-link diagrams in improving the efficiency and accuracy of manipulating and understanding the social network triads.
Paper Structure (24 sections, 5 equations, 5 figures, 3 tables, 1 algorithm)

This paper contains 24 sections, 5 equations, 5 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Triangle-based Visualization of Social Networks
  4. 3D Graph Visualization in VR
  5. Matrix Reordering
  6. Requirements
  7. The 3D Adjacency Matrix
  8. Representing triangles in a 3D Adjacency Matrix
  9. Reordering
  10. Implementation in VR
  11. User Exploration
  12. Implementation
  13. Evaluation
  14. Participants
  15. Set up
  16. ...and 9 more sections

Figures (5)

  • Figure 1: The transformation from a graph triangle in node-link form (a) to a cell in the 3D adjacency matrix (b).
  • Figure 2: The comparison of the two triangle patterns with their representations in the node-link diagram and the 3D adjacency matrix. In the 3D adjacency matrix, three triangles sharing a node (A1) are represented as the three cells on the same slice (B1); three triangles sharing an edge (A2) are represented as the three cells on the same straight line (B2).
  • Figure 3: The interactions provided by the controller.
  • Figure 4: (a) The 2D adjacency matrix slice colored with a yellow border contains the selected cell, with the intersection of axis $z$ as $w$. (b) All the triangles containing the $w$th node are shown with adding the symmetric triangles (on the left-bottom corner) after rotating the slice to the front of the user.
  • Figure 5: (a) The average time and the 95% confidence intervals. (b) The average accuracy cost and the 95% confidence intervals. (c) The average ratings of the questionnaire and 95% confidence intervals.