A partial edge drawing (PED) of a graph is a variation of a node-link diagram. PED draws a link, which is a partial visual representation of an edge, and reduces visual clutter of the node-link diagram. However, more time is required to read a PED to infer undrawn parts. The authors propose a morphing edge drawing (MED), which is a PED that changes with time. In MED, links morph between partial and complete drawings; thus, a reduced load for estimation of undrawn parts in a PED is expected. Herein, a formalization of MED is shown based on a formalization of PED. Then, requirements for the scheduling of morphing are specified. The requirements inhibit morphing from crossing and shorten the overall time for morphing the edges. Moreover, an algorithm for a scheduling method implemented by the authors is illustrated and the effectiveness of PED from a reading time viewpoint is shown through an experimental evaluation.
formalized the PED in their study @cite_6 ; our formalization of PED in is a modified version of their formalization. They added continuity of the omitted parts of links as a condition, we have incorporated this into the formalization herein. Moreover, although they focused on a layout without crossing stubs in PED, this study allows stub crossings. applied PED to directed graphs using tapered links @cite_1 . applied PED to weighted graphs by representing weights with edge colors @cite_9 .
@cite_9 @cite_1 @cite_6
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We investigate the readability of node-link diagrams for directed graphs when using partially drawn links instead of showing each link explicitly in its full length. Providing the complete link information between related nodes in a graph can lead to visual clutter caused by many edge crossings. To reduce visual clutter, we draw only partial links. Then, the question arises if such diagrams are still readable, understandable, and interpretable. As a step toward answering this question, we conducted a controlled user experiment with 42 participants to uncover differences in accuracy and completion time for three different tasks: identifying the existence of a direct link, the existence of an indirect connection with one intermediate node, and the node with the largest number of outgoing edges. Furthermore, we compared tapered and traditional edge representations, three different graph sizes, and six different link lengths. In all configurations, the nodes of the graph were placed according to the force-directed layout by Fruchterman and Reingold. One result of this study is that the characteristics of completion times and error rates depend on the type of task. A general observation is that partially drawn links can lead to shorter task completion times, which occurs for nearly all graph sizes, tasks, and both tapered and traditional edge representations. In contrast, there is a tendency toward higher error rates for shorter links, which in fact is task-dependent. 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.