Common quality metrics of graph drawing have been about the readability criteria, such as small number of edge crossings, small drawing area and small total edge length. Bold graph drawing considers more realistic drawings consisting of vertices as disks of some radius and edges as rectangles of some width. However, the relationship that links these readability criteria with the rendering criteria in node-link diagrams has still not been well-established. This paper introduces a model, so-called INKA (Ink-Active), that encapsulates mathematically the relationship between all common drawing factors. Consequently, we investigate our INKA model on several common drawing algorithms and real-world graphs.
Criteria for good' graph visualization have been investigated extensively @cite_5 . Graph drawing algorithms over the years typically take into account one or more aesthetic criteria for better of the drawing. These aesthetic criteria include, for example, enumerate minimizing the number of edge crossings @cite_14 ; minimizing the total area @cite_4 ; edge lengths should be short but not too short @cite_0 . Amongst these aesthetics, small number of edge crossings is one of the most common criterion from previous user studies @cite_1 . Besides, the amount of ink and minimum total edge length has been used in many layout algorithms; for example, @cite_22 @cite_6 @cite_7 @cite_23 . Achieving small total area is another common approach @cite_4 . Overall, improving multiple aesthetics can produce better graph drawings @cite_16 .
@cite_14 @cite_4 @cite_22 @cite_7 @cite_1 @cite_6 @cite_0 @cite_23 @cite_5 @cite_16
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Many automatic graph drawing algorithms implement only one or two aesthetic criteria since most aesthetics conflict with each other. Empirical research has shown that although those algorithms are based on different aesthetics, drawings produced by them have comparable effectiveness.The comparable effectiveness raises a question about the necessity of choosing one algorithm against another for drawing graphs when human performance is a main concern. In this paper, we argue that effectiveness can be improved when algorithms are designed by making compromises between aesthetics, rather than trying to satisfy one or two of them to the fullest. We therefore introduce a new algorithm: BIGANGLE. This algorithm produces drawings with multiple aesthetics being improved at the same time, compared to a classical spring algorithm. A user study comparing these two algorithms indicates that BIGANGLE induces a significantly better task performance and a lower cognitive load, therefore resulting in better graph drawings in terms of human cognitive efficiency.Our study indicates that aesthetics should not be considered separately. Improving multiple aesthetics at the same time, even to small extents, will have a better chance to make resultant drawings more effective. Although this finding is based on a study of algorithms, it also applies in general graph visualization and evaluation. Highlights? We have introduced cosine force, which is to increase the size of crossing angles. ? We have introduced sine force, which is to increase the angular resolution of vertices. ? We have introduced and implemented a force-directed algorithm, which improves multiple aesthetics at the same time. ? We have conducted a human study, which was the first to examine the collective effect of multiple aesthetics on humans. ? We have presented empirical evidence showing that improving multiple aesthetics produces better graph drawings. One of the main principles for the effective visualization of graphs is the avoidance of edge crossings. Around this problem, very active research has been performed with works ranging from combinatorics, to algorithmics, visualization effects, to psychological user studies. Recently, the pragmatic approach has been proposed to avoid crossings by drawing the edges only partially. Unfortunately, no formal model and efficient algorithms have been formulated to this end. We introduce the concept for drawings of graphs with partially drawn edges (PED). Therefore we consider graphs with and without given embedding and characterize PEDs with concepts like symmetry and homogeneity. For graphs without embedding we formulate a sufficient condition to guarantee a symmetric homogeneous PED, and identify a nontrivial graph class which has a symmetric homogeneous PED. For graphs with given layout we consider the variants of maximizing the shortest partially drawn edge and the total length respectively. Many real-world domains can be represented as large node-link graphs: backbone Internet routers connect with 70,000 other hosts, mid-sized Web servers handle between 20,000 and 200,000 hyperlinked documents, and dictionaries contain millions of words defined in terms of each other. Computational manipulation of such large graphs is common, but previous tools for graph visualization have been limited to datasets of a few thousand nodes. Visual depictions of graphs and networks are external representations that exploit human visual processing to reduce the cognitive load of many tasks that require understanding of global or local structure. We assert that the two key advantages of computer-based systems for information visualization over traditional paper-based visual exposition are interactivity and scalability. We also argue that designing visualization software by taking the characteristics of a target user's task domain into account leads to systems that are more effective and scale to larger datasets than previous work. This thesis contains a detailed analysis of three specialized systems for the interactive exploration of large graphs, relating the intended tasks to the spatial layout and visual encoding choices. We present two novel algorithms for specialized layout and drawing that use quite different visual metaphors. The H3 system for visualizing the hyperlink structures of web sites scales to datasets of over 100,000 nodes by using a carefully chosen spanning tree as the layout backbone, 3D hyperbolic geometry for a Focus+Context view, and provides a fluid interactive experience through guaranteed frame rate drawing. The Constellation system features a highly specialized 2D layout intended to spatially encode domain-specific information for computational linguists checking the plausibility of a large semantic network created from dictionaries. The Planet Multicast system for displaying the tunnel topology of the Internet's multicast backbone provides a literal 3D geographic layout of arcs on a globe to help MBone maintainers find misconfigured long-distance tunnels. Each of these three systems provides a very different view of the graph structure, and we evaluate their efficacy for the intended task. We generalize these findings in our analysis of the importance of interactivity and specialization for graph visualization systems that are effective and scalable. There is a large number of effective methodologies and algorithms for the creation of aesthetically pleasing graph drawings in two dimensions. However, representing graphs in three dimensions offers various benefits. The extra dimension gives greater flexibility for placing the vertices and edges of a graph and crossings can be always avoided. On the other hand new challenges arise: current output media have a two-dimensional nature and can only provide a limited resolution and display area. Thus, the resulting drawings become complex and difficult to survey. These disadvantages can be weakened by the use of navigational operations such as rotation, shifting and zooming. These operations enable an effective use of screen space and allow users to resolve ambiguities in large graphs while maintaining their overall mental map. The possibility of changing the viewpoint in 3D will also diminish the relevance of edge crossing in the (two-dimensional) screen representation of the graph.