text: 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.
  @cite_14: Various algorithms have been proposed for producing tidy drawings of trees–drawings that are aesthetically pleasing and use minimum drawing space. We show that these algorithms contain some difficulties that lead to aesthetically unpleasing, wider than necessary drawings. We then present a new algorithm with comparable time and storage requirements that produces tidier drawings. Generalizations to forests and m-ary trees are discussed, as are some problems in discretization when alphanumeric output devices are used.
  @cite_4: The state of the art in automatic graph drawing is reviewed, with special attention to the readability of information system diagrams. Existing results in the literature are compared, and a comprehensive algorithmic approach to the problem is proposed. The algorithm presented draws graphs on a grid and is suitable for both undirected graphs and mixed graphs that contain as subgraphs hierarchic structures. Several applications of GIOTTO, a graphic tool that embodies the aforementioned facility, are shown. >
  @cite_22: 
  @cite_7: Circular graph layout is a drawing scheme where all nodes are placed on the perimeter of a circle. An inherent issue with circular layouts is that the rigid restriction on node placement often gives rise to long edges and an overall dense drawing. We suggest here three independent, complementary techniques for lowering the density and improving the readability of circular layouts. First, a new algorithm is given for placing the nodes on the circle such that edge lengths are reduced. Second, we enhance the circular drawing style by allowing some of the edges to be routed around the exterior of the circle. This is accomplished with an algorithm for optimally selecting such a set of externally routed edges. The third technique reduces density by coupling groups of edges as bundled splines that share part of their route. Together, these techniques are able to reduce clutter, density and crossings compared with existing methods.
  @cite_1: In the creation of graph drawing algorithms and systems, designers claim that by producing layouts that optimise certain aesthetic qualities, the graphs are easier to understand. Such aesthetics include maximise symmetry, minimise edge crosses and minimise bends.
  @cite_6: We propose a heuristic for dynamic hierarchical graph drawing. Applications include incremental graph browsing and editing, display of dynamic data structures and networks, and browsing large graphs. The heuristic is an on-line interpretation of the static layout algorithm of Sugiyama, Togawa and Toda. It incorporates topological and geometric information with the objective of making layout animations that are incrementally stable and readable through long editing sequences. We measured the performance of a prototype implementation.
  @cite_0: Automatic graph layout is an important and long-studied problem. The basic straight-edge graph layout problem is to find spatial positions for the nodes of an input graph that maximize some measure of desirability. When graph layout is intended for human consumption, we call this measure of desirability an aesthetic. We seek an algorithm that produces graph layouts of high aesthetic quality not only for general graphs, but also for specific classes of graphs, such as trees and directed acyclic graphs. The Aesthetic Graph Layout (AGLO) approach described in this paper models graph layout as a multiobjective optimization problem, where the value of a layout is determined by multiple user-controlled layout aesthetics. The current AGLO algorithm combines the power and flexibility of the simulated annealing approach of Davidson and Harel (1989) with the relative speed of the method of Fruchterman and Reingold (1991). In addition, it is more general, and incorporates several new layout aesthetics to support new layout styles. Using these aesthetics, we are able to produce pleasing displays for graphs on which these other methods flounder.
  @cite_23: Graphs are often used to encapsulate relationships between objects. Node-link diagrams, commonly used to visualize graphs, suffer from visual clutter on large graphs. Edge bundling is an effective technique for alleviating clutter and revealing high-level edge patterns. Previous methods for general graph layouts either require a control mesh to guide the bundling process, which can introduce high variation in curvature along the bundles, or all-to-all force and compatibility calculations, which is not scalable. We propose a multilevel agglomerative edge bundling method based on a principled approach of minimizing ink needed to represent edges, with additional constraints on the curvature of the resulting splines. The proposed method is much faster than previous ones, able to bundle hundreds of thousands of edges in seconds, and one million edges in a few minutes.
  @cite_5: From the Publisher: This book is designed to describe fundamental algorithmic techniques for constructing drawings of graphs. Suitable as a book or reference manual, its chapters offer an accurate, accessible reflection of the rapidly expanding field of graph drawing.
  @cite_16: 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.
summary: 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 .