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_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_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_22: 
  @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.
summary: A number of graph drawing algorithms have aimed for a minimum total edge length, or more precisely, a minimum amount of ink. This criterion has been studied @cite_22 @cite_6 @cite_7 @cite_23 .