Persistent Homology Guided Force-Directed Graph Layouts

Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node arrangements that use local relationships in an attempt to reveal the global shape of the graph. However, clutter and overlap of unrelated structures can lead to confusing graph visualizations. This paper leverages the persistent homology features of an undirected graph as derived information for interactive manipulation of force-directed layouts. We first discuss how to efficiently extract 0-dimensional persistent homology features from both weighted and unweighted undirected graphs. We then introduce the interactive persistence barcode used to manipulate the force-directed graph layout. In particular, the user adds and removes contracting and repulsing forces generated by the persistent homology features, eventually selecting the set of persistent homology features that most improve the layout. Finally, we demonstrate the utility of our approach across a variety of synthetic and real datasets

Fast convergence layout algorithm for drawing graphs in marching-graph

Marching-Graph is a new visualization that integrates the graph metaphor and the spatial metaphor into a single visualization. It provides users with highly interactive maps for accessing the logical structures of information that has the geographical attributes. Instead of presenting known facts onto maps, it provides a mechanism for users to visually analyze and seek unknown knowledge through effective human-map interaction and navigation across different spaces. However, the traditional force-directed layout algorithms are very slow in reaching an equilibrium configuration of forces. They usually spend tens of seconds making the layout of a graph converge. Thus, those force-directed layout algorithms can not satisfy the requirement for drawing a sequence of graphs rapidly, while the users are quickly marching through the geographic regions. This paper proposes a fast convergence layout method that speeds up the interaction time while users are progressively exploring a sequence of graphs through a series of force-directed layouts in Marching-Graph. It essentially combines a radial tree drawing method and a force-directed graph drawing method to achieve the fast convergence of energy minimization

A Distributed Multilevel Force-directed Algorithm

The wide availability of powerful and inexpensive cloud computing services naturally motivates the study of distributed graph layout algorithms, able to scale to very large graphs. Nowadays, to process Big Data, companies are increasingly relying on PaaS infrastructures rather than buying and maintaining complex and expensive hardware. So far, only a few examples of basic force-directed algorithms that work in a distributed environment have been described. Instead, the design of a distributed multilevel force-directed algorithm is a much more challenging task, not yet addressed. We present the first multilevel force-directed algorithm based on a distributed vertex-centric paradigm, and its implementation on Giraph, a popular platform for distributed graph algorithms. Experiments show the effectiveness and the scalability of the approach. Using an inexpensive cloud computing service of Amazon, we draw graphs with ten million edges in about 60 minutes.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

The Galois Complexity of Graph Drawing: Why Numerical Solutions are Ubiquitous for Force-Directed, Spectral, and Circle Packing Drawings

Many well-known graph drawing techniques, including force directed drawings, spectral graph layouts, multidimensional scaling, and circle packings, have algebraic formulations. However, practical methods for producing such drawings ubiquitously use iterative numerical approximations rather than constructing and then solving algebraic expressions representing their exact solutions. To explain this phenomenon, we use Galois theory to show that many variants of these problems have solutions that cannot be expressed by nested radicals or nested roots of low-degree polynomials. Hence, such solutions cannot be computed exactly even in extended computational models that include such operations.Comment: Graph Drawing 201

Graph Layout Performance Comparisons of Force-Directed Algorithms

© 2018 Totem Publisher, Inc. All rights reserved. Due to force-directed algorithms’ capabilities of producing aesthetically pleasing graph layouts, which follow metrics for graph drawing aesthetics, these layouts have become the most common methods in the practical data visualization area. However, evaluating the performance of relevant algorithms remains a challenge, since graph layout quality is largely relying on aspects such as human intuition, personal judgment and methods’ pre-setting parameters. In addition, most aesthetics criteria of graph drawing conflict with each other. This study evaluated the performance measurements of four force-directed algorithms in terms of seven commonly applied aesthetic criteria based on practical raw data collected, and demonstrated the experimental framework. The early outcomes compared twenty final graph layouts and gave empirical evidences; the study may assist with future detailed force-directed algorithms selection based on users’ specific requirements