Quan Hoang Nguyen

On the faithfulness of graph visualizations

Readability criteria have been commonly used to measure the quality of graph visualizations. In this paper we argue that readability criteria, while necessary, are not sufficient. We propose a new kind of criterion, generically termed faithfulness, for evaluating graph layout methods. We propose a general model for quantifying faithfulness, and contrast it with the well established readability criteria. We use examples of multidimensional scaling, edge bundling and several other visualization metaphors (including matrix-based and map-based visualizations) to illustrate faithfulness.

TGI-EB: a new framework for edge bundling integrating topology, geometry and importance

Edge bundling methods became popular for visualising large dense networks; however, most of previous work mainly relies on geometry to define compatibility between the edges. In this paper, we present a new framework for edge bundling, which tightly integrates topology, geometry and importance. In particular, we introduce new edge compatibility measures, namely importance compatibility and topology compatibility. More specifically, we present four variations of force directed edge bundling method based on the framework: Centrality-based bundling, Radial bundling, Topology-based bundling, and Orthogonal bundling. Our experimental results with social networks, biological networks, geographic networks and clustered graphs indicate that our new framework can be very useful to highlight the most important topological skeletal structures of the input networks.

StreamEB: stream edge bundling

Graph streams have been studied extensively, such as for data mining, while fairly limitedly for visualizations. Recently, edge bundling promises to reduce visual clutter in large graph visualizations, though mainly focusing on static graphs. This paper presents a new framework, namely StreamEB, for edge bundling of graph streams, which integrates temporal, neighbourhood, data-driven and spatial compatibility for edges. Amongst these metrics, temporal and neighbourhood compatibility are introduced for the first time. We then present force-directed and tree-based methods for stream edge bundling. The effectiveness of our framework is then demonstrated using US flights data and Thompson-Reuters stock data.

Visual Analysis of History of World Cup: A Dynamic Network with Dynamic Hierarchy and Geographic Clustering

In this paper, we present new visual analysis methods for history of the FIFA World Cup competition data, a social network from Graph Drawing 2006 Competition. Our methods are based on the use of network analysis method, and new visualization methods for dynamic graphs with dynamic hierarchy and geographic clustering. More specifically, we derive a dynamic network with geographic clustering from the history of the FIFA World Cup competition data, based on who-beats-whom relationship. Combined with the centrality analysis (which defines dynamic hierarchy) and the use of the union of graphs (which determines the overall layout topology), we present three new visualization methods for dynamic graphs with dynamic hierarchy and geographic clustering: wheel layout, radial layout and hierarchical layout. Our experimental results show that our visual analysis methods can clearly reveal the overall winner of the World Cup competition history as well as the strong and weak countries. Furthermore, one can analyze and compare the performance of each country for each year along the context with their overall performance. This enables us to confirm the expected and discover the unexpected.

Large crossing angles in circular layouts

Recent empirical research has shown that increasing the angle of crossings reduces the effect of crossings and improves human readability [5]. In this paper, we introduce a post-processing algorithm, namely MAXCIR, that aims to increase crossing angles of circular layouts by using Quadratic Programming. Experimental results indicate that our method significantly increases crossing angles compared to the traditional equal-spacing algorithm, and that the running time is fairly negligible.

Circular right-angle crossing drawings in linear time

A common representational style for drawing graphs is the so-called circular drawings, where vertices are represented as points on a circle, and edges are represented as straight line segments. In such drawings, edges may cross; these edge crossings have a negative effect on human readability.Recent empirical research shows that increasing the angles of edge crossings reduces the negative effect of crossings on human readability. This result has motivated a number of recent investigations of right angle crossing graph drawings, where each crossing angle is π 2 .The main result of this paper is a characterization of graphs that admit a circular right angle crossing drawing. We present a linear-time algorithm for testing and constructing such a drawing of a graph, if it exists.Further, we give an upper bound on the number of edges in a circular right angle crossing drawing, and we note that the optimization problem of constructing circular drawings with large angle crossings can be formulated as a quadratic programming problem.

Circular Graph Drawings with Large Crossing Angles

This paper is motivated by empirical research that has shown that increasing the angle of edge crossings reduces the negative effect of crossings on human readability. We investigate circular graph drawings (where each vertex lies on a circle) with large crossing angles. In particular, we consider the case of right angle crossing (RAC) drawings, where each crossing angle is π/2.

Proxy Graph: Visual Quality Metrics of Big Graph Sampling

Data sampling has been extensively studied for large scale graph mining. Many analyses and tasks become more efficient when performed on graph samples of much smaller size. The use of proxy objects is common in software engineering for analysis and interaction with heavy objects or systems. In this paper, we coin the term ’proxy graph’ and empirically investigate how well a proxy graph visualization can represent a big graph. Our investigation focuses on proxy graphs obtained by sampling; this is one of the most common proxy approaches. Despite the plethora of data sampling studies, this is the first evaluation of sampling in the context of graph visualization. For an objective evaluation, we propose a new family of quality metrics for visual quality of proxy graphs. Our experiments cover popular sampling techniques. Our experimental results lead to guidelines for using sampling-based proxy graphs in visualization.

dNNG: Quality metrics and layout for neighbourhood faithfulness

This paper introduces a new kind of geometric graph, called the degree-sensitive neighbourhood graph (dNNG), for a more precise modelling of neighbourhoods. Based on dNNG, we define better shape-based metrics and then propose a neighbourhood-driven force-directed algorithm, called NEFO, for neighbourhood faithfulness. Our evaluation on both real-world and randomly generated graphs shows that the dNNG gives more effective shape-based measures when compared to existing geometric graphs. The NEFO algorithm is shown to be effective for improving neighbourhood faithfulness of graph drawings.

Drawing Big Graphs Using Spectral Sparsification

Spectral sparsification is a general technique developed by Spielman et al. to reduce the number of edges in a graph while retaining its structural properties. We investigate the use of spectral sparsification to produce good visual representations of big graphs. We evaluate spectral sparsification approaches on real-world and synthetic graphs. We show that spectral sparsifiers are more effective than random edge sampling. Our results lead to guidelines for using spectral sparsification in big graph visualization.