Graph Drawing Methods Research Articles

A Novel Metaphor Graph Drawing Method for Multidimensional Data Visualisation and Its Case Study on COVID-19 Vaccination Analysis

Visualisation techniques have been one of the best data processing and analysis methods in recent decades, and they have assisted in data understanding efforts in various fields. Visualisation techniques for low-dimensional data are well developed and applied in multiple sectors; however, multidimensional data visualisation techniques still present some limitations, such as inaccurate data comparison and perception, exaggerated visual differences, label occlusion, and overlap. This study addresses the pros and cons and proposes a novel graphical drawing method, the multidimensional rose chart. It adopts the design idea of the Nightingale rose chart, but overcomes relevant limitations. The main challenges of this area include the incomplete presentation of multidimensional data, the neglect of the linkage of multiple attributes, the inefficient use of space, and the lack of simplicity of the interface. Contributions include enriching the representations of multidimensional data through the use of colour shades, area, and height sizes to represent values; straightforward data attribute comparisons via graph nesting; and detailed attributes showing the use of specific value labels. To verify the preliminary validity of this method, we imported COVID-19 data into experiments and further compared the final layouts with traditional methods, such as the line chart, bar chart, tree, parallel coordinate chart, and Nightingale rose chart, as well as their structures, functionalities, clear advantages, and disadvantages. The experimental results show that multidimensional rose diagrams perform effectively in presenting multidimensional data when comparing other graph drawing methods in our case, and the outcomes match existing works' conclusions in related COVID-19 research sectors. This work has the potential to provide a suitable supplemental approach to the multidimensional data analysis.

A Coupling Path Analysis Method for High Power Microwave Interaction With Electronic Systems

In order to analyze the electromagnetic coupling path of real complex electronic system in high power microwave more conveniently and effectively, based on the electromagnetic topology theory, a signal flow graph drawing and simplification method based on coupling port is proposed, and the assignment principle of coupling path are given. The new method can satisfy the construction of signal flow graph in high power microwave environment with multiple interference sources and different bandwidths. Furthermore, aiming at the bidirectional coupling problem of signal flow graph and the shortest path calculation problem under different limit encountered in practical engineering application, this letter proposes an improved Floyd algorithm combined with double-sweep algorithm, which can solve the deficiency of traditional Dijkstra algorithm and Ford algorithm in solving the above engineering problems. Finally, the coupling path analysis method under the action of multiple interference sources is briefly discussed. The method proposed in this letter is more suitable for practical engineering, and it’s the base of the further electromagnetic protection work.

Applying Graph Centrality Metrics in Visual Analytics of Scientific Standard Datasets

Graphs are often used to model data with a relational structure and graphs are usually visualised into node-link diagrams for a better understanding of the underlying data. Node-link diagrams represent not only data entries in a graph, but also the relations among the data entries. Further, many graph drawing algorithms and graph centrality metrics have been successfully applied in visual analytics of various graph datasets, yet little attention has been paid to analytics of scientific standard data. This study attempts to adopt graph drawing methods (force-directed algorithms) to visualise scientific standard data and provide information with importance ‘ranking’ based on graph centrality metrics such as Weighted Degree, PageRank, Eigenvector, Betweenness and Closeness factors. The outcomes show that our method can produce clear graph layouts of scientific standard for visual analytics, along with the importance ‘ranking’ factors (represent via node colour, size etc.). Our method may assist users with tracking various relationships while understanding scientific standards with fewer relation issues (missing/wrong connection etc.) through focusing on higher priority standards.

Excelによるグラフの書き方 : パソコンによるデータ解析実践講座(1)

Excelによるグラフの書き方 : パソコンによるデータ解析実践講座(1)

Drawing clustered graphs by preserving neighborhoods

Weighted graphs with presumed cluster structure are challenging to many existing graph drawing methods, even though ways of visualizing such graphs would be much needed in complex networks research. In the field of dimension reduction, t-distibuted stochastic neighbor embedding (t-SNE) has proven successful in visualizing clustered data. Here, we extend t-SNE into graph-SNE (GSNE). Our method builds on the sensitivity of random walks to cluster structure in graphs. We use random walks to define a neighborhood probability that realizes the properties behind the success of t-SNE in visualizing clustered data sets: Gaussian-like behavior of neighborhood probabilities, adaptation to local edge density, and an adjustable granularity scale. We show that GSNE correctly visualizes artificial graphs where ground-truth cluster structure is known. Using real-world networks, we show that GSNE is able to produce meaningful visualizations that display plausible cluster structure which is not captured by state-of-the-art visualization methods.

Ivga: A fast force-directed method for interactive visualization of complex networks

Complex networks play a very important role in various fields of science as data structures, which aggregate information about mutual relationships between numerous objects. The structural properties of these large graphs can be scrutinized throughout their interactive visualization. However, visual analysis of complex networks consisting of |V|∼106+ vertices represents a great challenge for nowadays computer systems both from computational and storage perspective. Therefore, the existing graph drawing methods involving greater than O(|V|) time and space complexity cannot be regarded as promising tools in the advent of the Big Data era. We present here a new and very fast graph drawing method with O(|V|) time and space complexity – ivga (interactive visualization of graphs). We evaluate its usefulness and performance by testing ivga on the large complex networks from the Stanford Large Network Dataset Collection. We demonstrate that ivga allows for very fast interactive visualization of large graphs consisting of up to a few million vertices on a regular laptop what makes it very competitive to other state-of-art graph drawing methods. Particularly, we recommend ivga method for interactive visualization of large non-planar complex networks such as small-world and scale-free social networks. The main concept of ivga can be seriously considered in developing tools for visualization and analysis of really huge networks, with billions of vertices and edges, on Big Data systems.

Key-Node-Separated Graph Clustering and Layouts for Human Relationship Graph Visualization.

Many graph-drawing methods apply node-clustering techniques based on the density of edges to find tightly connected subgraphs and then hierarchically visualize the clustered graphs. However, users may want to focus on important nodes and their connections to groups of other nodes for some applications. For this purpose, it is effective to separately visualize the key nodes detected based on adjacency and attributes of the nodes. This article presents a graph visualization technique for attribute-embedded graphs that applies a graph-clustering algorithm that accounts for the combination of connections and attributes. The graph clustering step divides the nodes according to the commonality of connected nodes and similarity of feature value vectors. It then calculates the distances between arbitrary pairs of clusters according to the number of connecting edges and the similarity of feature value vectors and finally places the clusters based on the distances. Consequently, the technique separates important nodes that have connections to multiple large clusters and improves the visibility of such nodes' connections. To test this technique, this article presents examples with human relationship graph datasets, including a coauthorship and Twitter communication network dataset.

Attempt to Improve Subjective Graph Drawing Methods of Resilience

Attempt to Improve Subjective Graph Drawing Methods of Resilience

GosperMap: Using a Gosper Curve for Laying Out Hierarchical Data

The emergence of very large hierarchies that result from the increase in available data raises many problems of visualization and navigation. On data sets of such scale, classical graph drawing methods do not take advantage of certain human cognitive skills such as shape recognition. These cognitive skills could make it easier to remember the global structure of the data. In this paper, we propose a method that is based on the use of nested irregular shapes. We name it GosperMap as we rely on the use of a Gosper Curve to generate these shapes. By employing human perception mechanisms that were developed by handling, for example, cartographic maps, this technique facilitates the visualization and navigation of a hierarchy. An algorithm has been designed to preserve region containment according to the hierarchy and to set the leaves' sizes proportionally to a property, in such a way that the size of nonleaf regions corresponds to the sum of their children's sizes. Moreover, the input ordering of the hierarchy's nodes is preserved, i.e., the areas that represent two consecutive children of a node in the hierarchy are adjacent to one another. This property is especially useful because it guarantees some stability in our algorithm. We illustrate our technique by providing visualization examples of the repartition of tax money in the US over time. Furthermore, we validate the use of the GosperMap in a professional documentation context and show the stability and ease of memorization for this type of map.

A new force-directed graph drawing method based on edge–edge repulsion

The conventional force-directed methods for drawing undirected graphs are based on either vertex–vertex repulsion or vertex–edge repulsion. In this paper, we propose a new force-directed method based on edge–edge repulsion to draw graphs. In our framework, edges are modelled as charged springs, and a final drawing can be generated by adjusting positions of vertices according to spring forces and the repulsive forces, derived from potential fields, among edges. Different from the previous methods, our new framework has the advantage of overcoming the problem of zero angular resolution, guaranteeing the absence of any overlapping of edges incident to the common vertex. Given graph layouts probably generated by previous algorithms as the inputs to our algorithm, experimental results reveal that our approach produces promising drawings not only preserving the original properties of a high degree of symmetry and uniform edge length, but also preventing zero angular resolution and usually having larger average angular resolution. However, it should be noted that exhibiting a higher degree of symmetry and larger average angular resolution does not come without a price, as the new approach might result in the increase in undesirable overlapping of vertices as some of our experimental results indicate. To ease the problem of node overlapping, we also consider a hybrid approach which takes into account both edge–edge and vertex–vertex repulsive forces in drawing a graph.

Visualization methods for longitudinal social networks and stochastic actor-oriented modeling

AbstractAs a consequence of the rising interest in longitudinal social networks and their analysis, there is also an increasing demand for tools to visualize them. We argue that similar adaptations of state-of-the-art graph-drawing methods can be used to visualize both, longitudinal networks and predictions of stochastic actor-oriented models (SAOMs), the most prominent approach for analyzing such networks. The proposed methods are illustrated on a longitudinal network of acquaintanceship among university freshmen.

One- and two-page crossing numbers for some types of graphs

The simplest graph drawing method is that of putting the vertices of a graph on a line (spine) and drawing the edges as half-circles on k half planes (pages). Such drawings are called k-page book drawings and the minimal number of edge crossings in such a drawing is called the k-page crossing number. In a one-page book drawing, all edges are placed on one side of the spine, and in a two-page book drawing all edges are placed either above or below the spine. The one- and two-page crossing numbers of a graph provide upper bounds for the standard planar crossing. In this paper, we derive the exact one-page crossing numbers for four-row meshes, present a new proof for the one-page crossing numbers of Halin graphs, and derive the exact two-page crossing numbers for circulant graphs . We also give explicit constructions of the optimal drawings for each kind of graph.

J2.5dPathway: A 2.5D Visualization Tool to Display Selected Nodes in Biological Pathways, in Parallel Planes

Abstract The characteristics of metabolic pathways make them particularly amenable to layered graph drawing me-thods. This paper presents a visual Java-based tool for drawing and annotating biological pathways in two- and-a-half dimensions (2.5D) as an alternative to three- dimensional (3D) visualizations. Such visualization allows user to display different groups of clustered nodes, in different parallel planes, and to see a detailed view of a group of objects in focus and its place in the context of the whole system. This tool is an extended version of J2dPathway.Availability: An executable demo version is available to download from Sourceforge.net (http://sourceforge.net/ projects/j3dpathway/), with most of the metabolic path-ways included. A hands-on tutorial (in Korean) is also provided. However, our system still awaits full testing of its entire functionalities for practical usage. The current release lacks in some features, however will constantly updated. For academic purposes, contact neo@ewh-a.ac.kr for source codes, for possible collaboration.Keywords: metabolic pathways, pathway editor, visual-ization

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.

Energy Models for Graph Clustering

The cluster structure of many real-world graphs is of great interest, as the clusters may correspond e.g. to communities in social networks or to cohesive modules in software systems. Layouts can naturally represent the cluster structure of graphs by grouping densely connected nodes and separating sparsely connected nodes. This article introduces two energy models whose minimum energy layouts represent the cluster structure, one based on repulsion between nodes (like most existing energy models) and one based on repulsion between edges. The latter model is not biased towards grouping nodes with high degrees, and is thus more appropriate for the many real-world graphs with right-skewed degree distributions. The two energy models are shown to be closely related to widely used quality criteria for graph clusterings { namely the density of the cut, Shi and Malik’s normalized cut, and Newman’s modularity { and to objective functions optimized by eigenvector-based graph drawing methods.

An Improved Neural Network Model for the Two-Page Crossing Number Problem

The simplest graph drawing method is that of putting the vertices of a graph on a line and drawing the edges as half-circles either above or below the line. Such drawings are called two-page book drawings. The smallest number of crossings over all two-page drawings of a graph G is called the two-page crossing number of G. Cimikowski and Shope have solved the two-page crossing number problem for an n-vertex and m-edge graph by using a Hopfield network with 2 m neurons. We present here an improved Hopfield model with m neurons. The new model achieves much better performance in the quality of solutions and is more efficient than the model of Cimikowski and Shope for all graphs tested. The parallel time complexity of the algorithm, without considering the crossing number calculations, is O(m) for the new Hopfield model with m processors clearly outperforming the previous algorithm.

Drawing directed graphs using quadratic programming

We describe a new method for visualization of directed graphs. The method combines constraint programming techniques with a high performance force-directed placement (FDP) algorithm. The resulting placements highlight hierarchy in directed graphs while retaining useful properties of FDP; such as emphasis of symmetries and preservation of proximity relations. Our algorithm automatically identifies those parts of the digraph that contain hierarchical information and draws them accordingly. Additionally, those parts that do not contain hierarchy are drawn at the same quality expected from a nonhierarchical, undirected layout algorithm. Our experiments show that this new approach is better able to convey the structure of large digraphs than the most widely used hierarchical graph-drawing method. An interesting application of our algorithm is directional multidimensional scaling (DMDS). DMDS deals with low-dimensional embedding of multivariate data where we want to emphasize the overall flow in the data (e.g., chronological progress) along one of the axes.

Guest Editorial: InfoVis 2005

THREE papers in this issue of IEEE Transactions on Visualization and Computer Graphics (TVCG) are expanded versions of ones presented at InfoVis 2005. These examples of the cutting edge of information visualization research showcase the diversity and depth of the field, illustrating new display techniques as well as novel application domains for information visualization systems. The three papers focus on the visualization of three different styles of data: graph-based data, time series data, and categorical data. The techniques developed and described in these papers may also be applicable to data from a variety of problem areas and the authors include both design motivations in their work as well as illustrative examples of the application of the techniques. “Drawing Directed Graphs Using Quadratic Programming,” by Tim Dwyer, Yehuda Koren, and Kim Marriott, won the InfoVis 2005 Best Paper Award. In this paper, the authors introduce a new method for drawing directed graphs that combines constraint programming techniques with a high performance force-directed placement algorithm. The technique is useful for highlighting hierarchies in directed graphs while retaining beneficial properties of force-directed placement strategies such as proximity and symmetry relations. The authors also describe experiments that show this new visualization technique can convey the structure of large digraphs better than the most widely used hierarchical graph drawing method. “Designing for Social Data Analysis,” by Martin Wattenberg and Jesse Kriss, explores how an information visualization tool may become part of a dynamic online social environment. The authors focus on the area of baby naming and provide a delightful tool called the NameVoyager, a Web-based system that allows people to explore historical trends in the names that parents give to their children. The NameVoyager garnered huge interest on the Web when it was deployed and the authors explore how the system facilitates a form of social data analysis. The paper describes design decisions and implementation issues that arose for the system and it considers some of the reasons why the system became so popular. The paper concludes by discussing the design of an extension to the system for a more complex data set. “Parallel Sets: Interactive Exploration and Visual Analysis of Categorical Data,” by Robert Kosara, Fabian Bendix, and Helwig Hauser, applies a variation of the well-known parallel coordinates visualization technique for representing categorical data. The introduced technique shows data frequencies instead of individual data points and uses boxes and parallelograms within the parallel coordinates style plot. The authors include a rich set of interaction techniques with the visualization that allow viewers to examine many different perspectives on the data. They illustrate the power of their visualization through sample analysis scenarios with two example data sets.

WebInterViewer: visualizing and analyzing molecular interaction networks.

Molecular interaction networks, such as those involving protein-protein and protein-DNA interactions, often consist of thousands of nodes or even more, which severely limits the usefulness of many graph drawing tools because they become too slow for interactive analysis of the networks and because they produce cluttered drawings with many edge crossings. We present a new, fast-layout algorithm and its implementation called WebInterViewer for visualizing large-scale molecular interaction networks. WebInterViewer (i) finds a layout of the connected components of an entire network, (ii) finds a global layout of nodes with respect to pivot nodes within the connected components and (iii) refines the local layout of each connected component by first relocating midnodes with respect to their cutvertices and the direct neighbors of the cutvertices, and then relocating all nodes with respect to their neighbors within distance 2. The advantages of WebInterViewer over classical graph drawing methods include the facts that (i) it is an order of magnitude faster, (ii) it can visualize data directly from protein interaction databases and (iii) it provides several abstraction and comparison operations for analyzing large-scale biological networks effectively. WebInterViewer is accessible at http://interviewer.inha.ac.kr/.

Extraction of fuzzy clusters from weighted graphs

AbstractA type of graph spectral method is proposed in which the point ensemble is divided into fuzzy clusters based on a weighted adjoint matrix. In this method, the problem of extracting a fuzzy cluster from a point ensemble is formulated as an eigenvalue problem. This is repetitively applied so that clusters are extracted successively. First, the cluster extraction method based on the similarity matrix is applied to an undirected graph, which is then expanded to a digraph and an undirected bipartite graph, allowing the extraction of the link structure of the web page and image browsing search by keyword. Also, a type of graph drawing method is proposed in which the cluster structure is visualized by using correspondence analysis. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(1): 80–88, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1133