ZigzagNetVis: Suggesting temporal resolutions for graph visualization using zigzag persistence

TL;DR

ZigzagNetVis addresses the challenge of automatically selecting temporal resolutions for visualizing temporal graphs by leveraging zigzag persistent homology to detect topological changes across candidate resolutions. It builds zigzag filtrations, computes persistence barcodes, and uses the bottleneck distance $d_ ext{B}$ between consecutive resolutions to form a suggestion curve, identifying peaks that indicate meaningful structural shifts. The approach is complemented by a colored barcode timeline visualization that encodes connected-component evolution and node metadata, implemented in a web-based prototype with linked node-link diagrams. Evaluation includes a usage scenario on real-world school networks and a 27-participant user study, demonstrating that the method yields interpretable, pattern-rich resolutions and useful visual analysis tools.

Abstract

Temporal graphs are commonly used to represent complex systems and track the evolution of their constituents over time. Visualizing these graphs is crucial as it allows one to quickly identify anomalies, trends, patterns, and other properties that facilitate better decision-making. In this context, selecting an appropriate temporal resolution is essential for constructing and visually analyzing the layout. The choice of resolution is particularly important, especially when dealing with temporally sparse graphs. In such cases, changing the temporal resolution by grouping events (i.e., edges) from consecutive timestamps -- a technique known as timeslicing -- can aid in the analysis and reveal patterns that might not be discernible otherwise. However, selecting an appropriate temporal resolution is a challenging task. In this paper, we propose ZigzagNetVis, a methodology that suggests temporal resolutions potentially relevant for analyzing a given graph, i.e., resolutions that lead to substantial topological changes in the graph structure. ZigzagNetVis achieves this by leveraging zigzag persistent homology, a well-established technique from Topological Data Analysis (TDA). To improve visual graph analysis, ZigzagNetVis incorporates the colored barcode, a novel timeline-based visualization inspired by persistence barcodes commonly used in TDA. We also contribute with a web-based system prototype that implements suggestion methodology and visualization tools. Finally, we demonstrate the usefulness and effectiveness of ZigzagNetVis through a usage scenario, a user study with 27 participants, and a detailed quantitative evaluation.

Figures (15)

• Figure 1: A temporal graph of initial resolution $1$ (first row) and its partition and sliding-window timeslicing at resolution $r=2$ (second and third rows).
• Figure 2: Barcodes associated with a temporal graph at resolution $1$ and $2$. Each horizontal bar refers to a connected component throughout time.
• Figure 3: A pairing between the barcodes of Fig. \ref{['fig:barcodes']}. We outline in red the most distant paired bars (distance 3), causing the bottleneck distance.
• Figure 4: ZigzagNetVis workflow. (a) Users input a temporal graph and node metadata (optional). (b) We suggest resolutions using a four-step procedure. (c) Users visualize the graph using any resolution through the colored barcode and node-link diagrams, visualizations that compose our prototype.
• Figure 5: A suggestion curve in red, its corresponding normalized suggestion curve in blue (for partition timeslicing), and the curve $i\mapsto r_{i}$ in black.