Fast Spherical Drawing of Triangulations: An Experimental Study of Graph Drawing Tools

We consider the problem of computing a spherical crossing-free geodesic drawing of a planar graph: this problem, as well as the closely related spherical parameterization problem, has attracted a lot of attention in the last two decades both in theory and in practice, motivated by a number of applications ranging from texture mapping to mesh remeshing and morphing. Our main concern is to design and implement a linear time algorithm for the computation of spherical drawings provided with theoretical guarantees. While not being aesthetically pleasing, our method is extremely fast and can be used as initial placer for spherical iterative methods and spring embedders. We provide experimental comparison with initial placers based on planar Tutte parameterization. Finally we explore the use of spherical drawings as initial layouts for (Euclidean) spring embedders: experimental evidence shows that this greatly helps to untangle the layout and to reach better local minima

The spring bounces back: introducing the strain elevation tension spring embedding algorithm for network representation

This paper introduces the strain elevation tension spring embedding (SETSe) algorithm. SETSe is a novel graph embedding method that uses a physical model to project feature-rich networks onto a manifold with semi-Euclidean properties. Due to its method, SETSe avoids the tractability issues faced by traditional force-directed graphs, having an iteration time and memory complexity that is linear to the number of edges in the network. SETSe is unusual as an embedding method as it does not reduce dimensionality or explicitly attempt to place similar nodes close together in the embedded space. Despite this, the algorithm outperforms five common graph embedding algorithms, on graph classification and node classification tasks, in low-dimensional space. The algorithm is also used to embed 100 social networks ranging in size from 700 to over 40,000 nodes and up to 1.5 million edges. The social network embeddings show that SETSe provides a more expressive alternative to the popular assortativity metric and that even on large complex networks, SETSe’s classification ability outperforms the naive baseline and the other embedding methods in low-dimensional representation. SETSe is a fast and flexible unsupervised embedding algorithm that integrates node attributes and graph topology to produce interpretable results

Graph layout for applications in compiler construction

We address graph visualization from the viewpoint of compiler construction. Most data structures in compilers are large, dense graphs such as annotated control flow graph, syntax trees, dependency graphs. Our main focus is the animation and interactive exploration of these graphs. Fast layout heuristics and powerful browsing methods are needed. We give a survey of layout heuristics for general directed and undirected graphs and present the browsing facilities that help to manage large structured graph

The spring bounces back: Introducing the Strain Elevation Tension Spring embedding algorithm for network representation

This paper introduces the Strain Elevation Tension Spring embedding (SETSe) algorithm, a graph embedding method that uses a physics model to create node and edge embeddings in undirected attribute networks. Using a low-dimensional representation, SETSe is able to differentiate between graphs that are designed to appear identical using standard network metrics such as number of nodes, number of edges and assortativity. The embeddings generated position the nodes such that sub-classes, hidden during the embedding process, are linearly separable, due to the way they connect to the rest of the network. SETSe outperforms five other common graph embedding methods on both graph differentiation and sub-class identification. The technique is applied to social network data, showing its advantages over assortativity as well as SETSe's ability to quantify network structure and predict node type. The algorithm has a convergence complexity of around $\mathcal{O}(n^2)$, and the iteration speed is linear ($\mathcal{O}(n)$), as is memory complexity. Overall, SETSe is a fast, flexible framework for a variety of network and graph tasks, providing analytical insight and simple visualisation for complex systems.Comment: 27 pages; 7000 word

Balanced Schnyder woods for planar triangulations: an experimental study with applications to graph drawing and graph separators

In this work we consider balanced Schnyder woods for planar graphs, which are Schnyder woods where the number of incoming edges of each color at each vertex is balanced as much as possible. We provide a simple linear-time heuristic leading to obtain well balanced Schnyder woods in practice. As test applications we consider two important algorithmic problems: the computation of Schnyder drawings and of small cycle separators. While not being able to provide theoretical guarantees, our experimental results (on a wide collection of planar graphs) suggest that the use of balanced Schnyder woods leads to an improvement of the quality of the layout of Schnyder drawings, and provides an efficient tool for computing short and balanced cycle separators.Comment: Appears in the Proceedings of the 27th International Symposium on Graph Drawing and Network Visualization (GD 2019

Graph layout for applications in compiler construction

We address graph visualization from the viewpoint of compiler construction. Most data structures in compilers are large, dense graphs such as annotated control flow graph, syntax trees, dependency graphs. Our main focus is the animation and interactive exploration of these graphs. Fast layout heuristics and powerful browsing methods are needed. We give a survey of layout heuristics for general directed and undirected graphs and present the browsing facilities that help to manage large structured graph

Strain Elevation Tension Spring embedding and Cascading failures on the power-grid

Understanding the dynamics and properties of networks is of great importance in our highly connected data-driven society. When the networks relate to infrastructure, such understanding can have a substantial impact on public welfare. As such, there is a need for algorithms that can provide insights into the observable and latent properties of these structures. This thesis presents a novel embedding algorithm: the Strain Elevation Tension Spring embedding (SETSe), as a method of understanding complex networks. The algorithm is a deterministic physics model that incorporates both node and edge features into the final embedding. SETSe distinguishes itself from most embeddings methods by not having a loss function in the conventional sense and by not trying to place similar nodes close together. Instead, SETSe acts as a smoothing function for node features across the network topology. This approach produces embeddings that are intuitive and interpretable. In this thesis, I demonstrate how SETSe outperforms alternative embedding methods on node level and graph level tasks using networks made from stochastic block models and social networks with over 40,000 nodes and over 1 million edges. I also highlight a weakness of traditional methods to analysing cascading failures on power grids and demonstrate that SETSe is not susceptible to such issues. I then show how SETSe can be used as a measure of robustness in addition to providing a means to create interpretable maps in the geographical space given its smoothing embedding method. The framework has been made widely available through two open source R packages contributions, 1) the implementation of SETSe ("rsetse" on CRAN), and 2) a package for analysing cascading failures on power grids