# Similarity-Driven Edge Bundling: Data-Oriented Clutter Reduction in Graphs Layouts
## 5 Use Cases
### Multi-Scale Edge Bundling Visualization  
Finally, we discuss how SDEB can be used to provide insights into graphs using a multi-scale approach. In this use case, we use the _Amazon Product co-purchasing Network_ (**amazon**) dataset [47]. This dataset represents more than 500,000 products from Amazon's website and associate information, such as product category, similar products, and reviews written by clients. We consider only grocery products to focus our analysis, resulting in a graph with 8700 vertices (products) and 129,407 edges connecting products purchased together. Similarity among products is calculated using the reviews published by customers.  
To create a multi-scale representation, we define a threshold \(\tau\) limiting the maximum depth of the _backbone_ to be used. Intermediate or data (products) vertices deeper than \(\tau\) are filtered out from the visualization and represented by their closest visible ancestors, composing a cluster of similar vertices. Edges connecting elements inside the same cluster are also removed from the visual representation. Figure 16 shows three layouts, varying the maximum depth in which the _backbone_ is rendered. When \(\tau=8\) (Figure 16a), only 248 vertices are visible, with almost all vertices representing clusters of products. The layout with \(\tau=12\) shows 2108 vertices (Figure 16b) and the layout with \(\tau=16\) shows 5856 (Figure 16c), which means that only few vertices still represent clusters of products. In such cases, we also observe the congestion of edges inside more populated groups.  
Figure 16: Multi-scale bundling of the **amazon** dataset. As more information is added to the graph representation (larger \(\tau\)), it becomes evident that only few vertices represent clusters of products.  
Figure 15: Small-multiples visualization for multiple _voting frames_ of the **#NABABallot** dataset. The same dominant patterns of Figure 14 are visible but their density change over time, a pattern potentially related to game days or marketing campaigns asking for votes.  
Users can change \(\tau\) to explore the graph bundling in different levels of detail. In Figure 17 we fix \(\tau=10\) and tag the 63 visible groups of products with the most common topics found in their reviews. By labeling the groups, we can see which products belong to each group. Some neighbor groups share the same topics, indicating that they were defined at a higher level and refined in the lower ones. For example, all groups in the bottom-left branch are labeled with \"Tea\". Another observable behavior is that the first division segments liquid and solid groceries. The bundling layout was created using the parameters \(\beta=0.95\), \(\gamma=0.1\) and \(\Delta=0.13\). This configuration also highlights dense groups, with more connections among their elements and their neighbors.  
This example shows that the multi-scale layouts produced by our technique facilitate the detection of vertices and clusters. For comparison, Figure 18 presents the original graph (using straight lines to represent the edges) and the edge bundling layout produced by CUBu, the fastest technique in the state-of-the-art. Although CUBu generates the bundling in 1.437 s, the layout could not organize edges into meaningful bundles, and the clutter reduction is not as significant as in the layout produced by our technique. Moreover, vertices are hidden in both layouts, especially in dense areas of edges, impacting the analysis and insights that can be derived. Our technique took around 100 s to create the backbone and 55 s to render the full graph. However, it creates a less cluttered layout where groups of products and their connections are clear.  
Figure 17: SDEB layout of the dataset **amazon** dataset. The visualization is limited at the 9 th graph level. Vertices were divided into 63 groups and each group is highlighted with its most common topics, extracted from the set of reviews written by customers.