AdaMotif: Graph Simplification via Adaptive Motif Design

TL;DR

AdaMotif addresses the challenge of visualizing large graphs by replacing subgraph groups with adaptive motifs derived from clustered subgraphs, thereby reducing visual clutter while preserving essential community information. The method integrates community detection, subgraph clustering, and similarity/difference-aware layouts to automatically generate motifs that summarize both global topology and local structure. Key contributions include a novel adaptive motif design framework, a similarity-aware representative subgraph layout, and a difference-aware individual subgraph layout, validated through real-world case studies and a user study that show improved readability and task performance. The approach is particularly effective for revealing community structures in large graphs, with potential extensions to directed and dynamic graphs and opportunities for interactive exploration to mitigate edge-information loss.

Abstract

With the increase of graph size, it becomes difficult or even impossible to visualize graph structures clearly within the limited screen space. Consequently, it is crucial to design effective visual representations for large graphs. In this paper, we propose AdaMotif, a novel approach that can capture the essential structure patterns of large graphs and effectively reveal the overall structures via adaptive motif designs. Specifically, our approach involves partitioning a given large graph into multiple subgraphs, then clustering similar subgraphs and extracting similar structural information within each cluster. Subsequently, adaptive motifs representing each cluster are generated and utilized to replace the corresponding subgraphs, leading to a simplified visualization. Our approach aims to preserve as much information as possible from the subgraphs while simplifying the graph efficiently. Notably, our approach successfully visualizes crucial community information within a large graph. We conduct case studies and a user study using real-world graphs to validate the effectiveness of our proposed approach. The results demonstrate the capability of our approach in simplifying graphs while retaining important structural and community information.

Figures (10)

• Figure 1: Our AdaMotif framework overview: (a) the original force-directed layout graph d3-component; (b) partitioning (a) into subgraphs annotated with different colors; (c) clustering subgraphs into categories indicated by gray dashed boxes, selecting a cluster center as the representative subgraph for each category, and further clustering these representatives into categories indicated by gray dashed boxes; (d) laying out representative subgraphs based on the super-graph to show similarities and then laying out individual subgraphs to show differences. The red dashed ovals highlight the graph differences and their encoding in our results; (e) generating adaptive motifs with colors encoding the categories; (f) the final simplified graph.
• Figure 2: An example of the similarity-aware representative subgraph layout algorithm. Nodes with the same color indicate that they are matched through graph alignment. In (c), the yellow nodes on the periphery are placed in the center of the generated super-graph in (d). This is not due to their importance, but because the positions of the blue and yellow nodes were swapped. The blue nodes needed to be on the periphery to connect to the unmatched gray nodes. This did not significantly impact the final similarity-aware layout result in (e).
• Figure 3: An example of the difference-aware individual subgraph layout algorithm. Nodes with the same color indicate that they are matched through graph alignment. The red dashed ovals highlight the graph differences in (c) and their encoding in (d).
• Figure 4: Five node encoding types in the difference-aware individual subgraph layout algorithm: (a) unaligned nodes; (b) aligned nodes not linked to unaligned nodes; (c)-(e) aligned nodes linked to unaligned nodes, and a wider outer ring indicates more linked unaligned nodes.
• Figure 5: Cpan dataset heymann2009cpan: (a) the original graph with three communities in different colors; (b) the simplified graph with three motifs highlighted with gray boxes; (c), (e), and (g) separately displayed communities in different colors in (a); (d), (f), and (h) separately displayed motifs highlighted with gray boxes in (b). (c) and (d) represent the same community. (e) and (f) represent the same community. (g) and (h) represent the same community.