Graph drawing and visualisation techniques are important tools for the exploratory analysis of complex systems. While these methods are regularly applied to visualise data on complex networks, we increasingly have access to time series data that can be modelled as temporal networks or dynamic graphs. In such dynamic graphs, the temporal ordering of time-stamped edges determines the causal topology of a system, i.e. which nodes can directly and indirectly influence each other via a so-called causal path. While this causal topology is crucial to understand dynamical processes, the role of nodes, or cluster structures, we lack graph drawing techniques that incorporate this information into static visualisations. Addressing this gap, we present a novel dynamic graph drawing algorithm that utilises higher-order graphical models of causal paths in time series data to compute time-aware static graph visualisations. These visualisations combine the simplicity of static graphs with a time-aware layout algorithm that highlights patterns in the causal topology that result from the temporal dynamics of edges.
Despite the advances outlined above, recognizing patterns in animation-based visualisations of dynamic graphs remains a considerable cognitive challenge for users. Moreover, it is difficult to embed dynamic graph animations into scholarly articles, books, or posters, which often limits their use in science and engineering to illustrative supplementary material. Addressing these issues, a second line of research focuses on methods to visualize dynamic graphs in terms of , which map the time dimension of dynamic graphs to a spatial dimension that can be embedded into a static visualisation. Examples includes widely-used directed acyclic of time-unfolded graph representations of dynamic graphs @cite_7 @cite_27 , or @cite_28 @cite_4 @cite_31 , sequences of layered adjacencies @cite_54 , stacked 3D representations where consecutive time slices are arranged along a third dimension @cite_2 . While recent works have proposed circular representations that scale to larger time series @cite_51 , the application of visualisations that map time to a spatial dimension is limited to a moderately large number of time stamps. Moreover, to the best of our knowledge, the effects of the chronological order of edges on the causal topology has not been considered in static visualisations of dynamic graphs.
@cite_4 @cite_7 @cite_28 @cite_54 @cite_27 @cite_2 @cite_31 @cite_51
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Graph drawing algorithms have classically addressed the layout of static graphs. However, the need to draw evolving or dynamic graphs has brought into question many of the assumptions, conventions and layout methods designed to date. For example, social scientists studying evolving social networks have created a demand for visual representations of graphs changing over time. Two common approaches to represent temporal information in graphs include animation of the network and use of static snapshots of the network at different points in time. Here, we report on two experiments, one in a laboratory environment and another using an asynchronous remote web-based platform, Mechanical Turk, to compare the efficiency of animated displays versus static displays. Four tasks are studied with each visual representation, where two characterise overview level information presentation, and two characterise micro level analytical tasks. For the tasks studied in these experiments and within the limits of the experimental system, the results of this study indicate that static representations are generally more effective particularly in terms of time performance, when compared to fully animated movie representations of dynamic networks. Dynamic graph visualization focuses on the challenge of representing the evolution of relationships between entities in readable, scalable and effective diagrams. This work surveys the growing number of approaches in this discipline. We derive a hierarchical taxonomy of techniques by systematically categorizing and tagging publications. While static graph visualizations are often divided into node-link and matrix representations, we identify the representation of time as the major distinguishing feature for dynamic graph visualizations: either graphs are represented as animated diagrams or as static charts based on a timeline. Evaluations of animated approaches focus on dynamic stability for preserving the viewer's mental map or, in general, compare animated diagrams to timeline-based ones. A bibliographic analysis provides insights into the organization and development of the field and its community. Finally, we identify and discuss challenges for future research. We also provide feedback from experts, collected with a questionnaire, which gives a broad perspective of these challenges and the current state of the field. Dynamic graph visualization focuses on the challenge of representing the evolution of relationships between en- tities in readable, scalable, and effective diagrams. This work surveys the growing number of approaches in this discipline. We derive a hierarchical taxonomy of techniques by systematically categorizing and tagging publica- tions. While static graph visualizations are often divided into node-link and matrix representations, we identify the representation of time as the major distinguishing feature for dynamic graph visualizations: either graphs are represented as animated diagrams or as static charts based on a timeline. Evaluations of animated approaches focus on dynamic stability for preserving the viewer's mental map or, in general, compare animated diagrams to timeline-based ones. Finally, we identify and discuss challenges for future research. We present a novel dynamic graph visualization technique based on node-link diagrams. The graphs are drawn side-byside from left to right as a sequence of narrow stripes that are placed perpendicular to the horizontal time line. The hierarchically organized vertices of the graphs are arranged on vertical, parallel lines that bound the stripes; directed edges connect these vertices from left to right. To address massive overplotting of edges in huge graphs, we employ a splatting approach that transforms the edges to a pixel-based scalar field. This field represents the edge densities in a scalable way and is depicted by non-linear color mapping. The visualization method is complemented by interaction techniques that support data exploration by aggregation, filtering, brushing, and selective data zooming. Furthermore, we formalize graph patterns so that they can be interactively highlighted on demand. A case study on software releases explores the evolution of call graphs extracted from the JUnit open source software project. In a second application, we demonstrate the scalability of our approach by applying it to a bibliography dataset containing more than 1.5 million paper titles from 60 years of research history producing a vast amount of relations between title words.