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1. Stress-Plus-X (SPX) Graph Layout

   https://doi.org/10.1007/978-3-030-35802-0_23  

   Devkota, S; Ahmed, R; De Luca, F; Isaacs, K; Kobourov, S (January 2020, 27th International Symposium on Graph Drawing and Network Visualization (GD))

   Stress, edge crossings, and crossing angles play an important role in the quality and readability of graph drawings. Most standard graph drawing algorithms optimize one of these criteria which may lead to layouts that are deficient in other criteria. We introduce an optimization framework, Stress-Plus-X (SPX), that simultaneously optimizes stress together with several other criteria: edge crossings, minimum cross- ing angle, and upwardness (for directed acyclic graphs). SPX achieves results that are close to the state-of-the-art algorithms that optimize these metrics individually. SPX is flexible and extensible and can optimize a subset or all of these criteria simultaneously. Our experimental analysis shows that our joint optimization approach is successful in drawing graphs with good performance across readability criteria. 

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2. The Multi-Dimensional Landscape of Graph Drawing Metrics

   Mooney, Gavin; Purchase, Helen; Wybrow, Michael; Kobourov, Stephen (April 2024, 17th IEEE Pacific Visualization Symposium (PACIFICVIS))

   Any graph drawing can be characterised by a range of computational aesthetic metrics. For example, a given drawing might be described as having eight crossings, a mean angular resolution of 0.34, and an edge orthogonality value of 0.72. However, without knowing the distribution of these metrics it is hard to compare the quality of drawings of different graphs, nor know whether a given drawing is typical or an outlier within the space of all possible drawings. This paper explores the range and distribution of ten normalised graph drawing layout metrics, based on graphs created by six graph generation algorithms and drawings created by six popular layout algorithms. We include the “Rome" and “North" graph repositories in our analysis. Our exploration of the multi-dimensional aesthetics space allows for comparisons between the graph drawing algorithms, highlighting those that cover larger or smaller volumes of the aesthetics space. We calculate the correlation coefficients between the metrics, indicating those that may conflict with each other (negatively correlated), and those that may be redundant (positively correlated). Our results will be useful as the basis for simulated annealing or gradient descent layout algorithms, for identifying the best layout algorithms for producing a specified combination and range of aesthetics, and for informing experimental controls in human empirical studies. 

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3. Graph drawing via gradient descent,

   Ahmed, R; De Luca, F; Devkota, S; Kobourov, S; Li, M (October 2020, 28th International Symposium on Graph Drawing and Network Visualization (GD))

   Readability criteria, such as distance or neighborhood preservation, are often used to optimize node-link representations of graphs to enable the comprehension of the underlying data. With few exceptions, graph drawing algorithms typically optimize one such criterion, usually at the expense of others. We propose a layout approach, Graph Drawing via Gradient Descent, (GD)^2, that can handle multiple readability criteria. (GD)^2 can optimize any criterion that can be described by a smooth function. If the criterion cannot be captured by a smooth function, a non-smooth function for the criterion is combined with another smooth function, or auto-differentiation tools are used for the optimization. Our approach is flexible and can be used to optimize several criteria that have already been considered earlier (e.g., obtaining ideal edge lengths, stress, neighborhood preservation) as well as other criteria which have not yet been explicitly optimized in such fashion (e.g., vertex resolution, angular resolution, aspect ratio). We provide quantitative and qualitative evidence of the effectiveness of (GD)^2 with experimental data and a functional prototype: http://hdc.cs.arizona.edu/~mwli/graph-drawing/ 

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4. A Scalable Method for Readable Tree Layouts

   https://doi.org/10.1109/TVCG.2023.3274572  

   Gray, Kathryn; Li, Mingwei; Ahmed, Reyan; Rahman, Md. Khaledur; Azad, Ariful; Kobourov, Stephen; Börner, Katy (April 2023, IEEE Transactions on Visualization and Computer Graphics)

   Large tree structures are ubiquitous and real-world relational datasets often have information associated with nodes (e.g., labels or other attributes) and edges (e.g., weights or distances) that need to be communicated to the viewers. Yet, scalable, easy to read tree layouts are difficult to achieve. We consider tree layouts to be readable if they meet some basic requirements: node labels should not overlap, edges should not cross, edge lengths should be preserved, and the output should be compact. There are many algorithms for drawing trees, although very few take node labels or edge lengths into account, and none optimizes all requirements above. With this in mind, we propose a new scalable method for readable tree layouts. The algorithm guarantees that the layout has no edge crossings and no label overlaps, and optimizing one of the remaining aspects: desired edge lengths and compactness. We evaluate the performance of the new algorithm by comparison with related earlier approaches using several real-world datasets, ranging from a few thousand nodes to hundreds of thousands of nodes. Tree layout algorithms can be used to visualize large general graphs, by extracting a hierarchy of progressively larger trees. We illustrate this functionality by presenting several map-like visualizations generated by the new tree layout algorithm. 

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5. DeepGD: A Deep Learning Framework for Graph Drawing Using GNN

   Xiaoqi Wang, Kevin Yen (September 2021, IEEE computer graphics and applications)

   Abstract—In the past decades, many graph drawing techniques have been proposed for generating aesthetically pleasing graph layouts. However, it remains a challenging task since different layout methods tend to highlight different characteristics of the graphs. Recently, studies on deep learning based graph drawing algorithm have emerged but they are often not generalizable to arbitrary graphs without re-training. In this paper, we propose a Convolutional Graph Neural Network based deep learning framework, DeepGD, which can draw arbitrary graphs once trained. It attempts to generate layouts by compromising among multiple pre-specified aesthetics considering a good graph layout usually complies with multiple aesthetics simultaneously. In order to balance the trade-off, we propose two adaptive training strategies which adjust the weight factor of each aesthetic dynamically during training. The quantitative and qualitative assessment of DeepGD demonstrates that it is capable of drawing arbitrary graphs effectively, while being flexible at accommodating different aesthetic criteria. 

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