Similarity-Driven Edge Bundling: Data-Oriented Clutter Reduction in Graphs Layouts
Abstract
:1. Introduction
- An approach to creating graph bundling layouts in which the bundles are defined based on similarity relationships;
- A strategy to explore bundling layouts using a multiscale approach using aggregation and adaptative bundling parameters; and
- A stable strategy to bundle edges in graphs with time-varying topology.
2. Related Work
3. Similarity-Driven Edge Bundling (SDEB)
3.1. Backbone Construction
Similarity Tree (STree)
Algorithm 1 Similarity Tree (STree) algorithm. | |
functionSimilarityTree(D) | |
▹ assign all data objects/vertices to the first cluster C | |
Centroid(C) | ▹ create a tree T and set its root as the centroid of C (first intermediate node) |
SimilarityTreeRec(C, ) | ▹ generate the complete tree |
return T | |
end function | |
functionSimilarityTreeRec(C, ) | |
if then | ▹ If the input cluster C has more than one data object |
Split(C) | ▹ split C into two clusters |
Centroid() | ▹ set the left child of as the centroid of |
Centroid() | ▹ set the right child of as the centroid of |
SimilarityTreeRec(, ) | |
SimilarityTreeRec(, ) | |
end if | |
end function | |
functionSplit(C) | |
Pivots(C) | ▹ select initial pivots for splitting |
while MAX_ITERATIONS do | |
▹ Initialize the cluster | |
▹ Initialize the cluster | |
for all do | |
if then | |
▹ add to cluster | |
else | |
▹ add to cluster | |
end if | |
end for | |
Centroid() | ▹ update the pivot of |
Centroid() | ▹ update the pivot of |
end while | |
return | |
end function |
3.2. Graph Drawing
3.2.1. Positioning the Vertices
Algorithm 2 Swapping H-tree algorithm. | |
functionSwappingHTree(T) | |
SwappingHTreeRec(, , ) | |
return T | |
end function | |
functionSwappingHTreeRec(, , ) | |
if then | ▹ Set the root vertex to the layout’s center |
else | |
if then | ▹ If it is an horizontal placement |
if is left child then | |
else | |
end if | |
else | ▹ If it is an vertical placement |
if is left child then | |
else | |
end if | |
end if | |
Swap() | ▹ Swap the children of if it improves the layout |
SwappingHTreeRec() | |
SwappingHTreeRec() | |
end if | |
end function | |
functionSwap() | |
if then | ▹ If the parent of is a left child |
if then | |
SwapSiblings(, ) | |
end if | |
else | ▹ If the parent of is a right child |
if then | |
SwapSiblings(, ) | |
end if | |
end if | |
end function |
3.2.2. Edge Bending
4. Results and Evaluation
4.1. Quantitative Analysis
4.1.1. Backbone Evaluation
4.1.2. Swapping Evaluation
4.2. Qualitative Analysis
4.2.1. Bundling Evaluation
4.2.2. Bundling Enhancements
5. Use Cases
5.1. Edge Bundling Simplification
5.2. Dynamic Edge Bundling Visualization
5.3. Multi-Scale Edge Bundling Visualization
6. Discussions and Limitations
7. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Sikansi, F.; da Silva, R.R.O.; Cantareira, G.D.; Etemad, E.; Paulovich, F.V. Similarity-Driven Edge Bundling: Data-Oriented Clutter Reduction in Graphs Layouts. Algorithms 2020, 13, 290. https://doi.org/10.3390/a13110290
Sikansi F, da Silva RRO, Cantareira GD, Etemad E, Paulovich FV. Similarity-Driven Edge Bundling: Data-Oriented Clutter Reduction in Graphs Layouts. Algorithms. 2020; 13(11):290. https://doi.org/10.3390/a13110290
Chicago/Turabian StyleSikansi, Fabio, Renato R. O. da Silva, Gabriel D. Cantareira, Elham Etemad, and Fernando V. Paulovich. 2020. "Similarity-Driven Edge Bundling: Data-Oriented Clutter Reduction in Graphs Layouts" Algorithms 13, no. 11: 290. https://doi.org/10.3390/a13110290
APA StyleSikansi, F., da Silva, R. R. O., Cantareira, G. D., Etemad, E., & Paulovich, F. V. (2020). Similarity-Driven Edge Bundling: Data-Oriented Clutter Reduction in Graphs Layouts. Algorithms, 13(11), 290. https://doi.org/10.3390/a13110290