Detecting and visualizing what are the most relevant changes in an evolving network is an open challenge in several domains. We present a fast algorithm that filters subsets of the strongest nodes and edges representing an evolving weighted graph and visualize it by either creating a movie, or by streaming it to an interactive network visualization tool. The algorithm is an approximation of exponential sliding time-window that scales linearly with the number of interactions. We compare the algorithm against rectangular and exponential sliding time-window methods. Our network filtering algorithm: (i) captures persistent trends in the structure of dynamic weighted networks, (ii) smoothens transitions between the snapshots of dynamic network, and (iii) uses limited memory and processor time. The algorithm is publicly available as open-source software.
More in general, there are several open fronts in empirical research in graph visualization to identify the impact of certain factors on the quality of the animation (e.g., speed @cite_69 , interactivity @cite_36 ). An extensive overview of this aspect has been conducted recently by @cite_15 . Methods to preserve the stability of nodes and the consistency of the network structure leveraging hierarchical organization on nodes have been proposed @cite_5 @cite_14 @cite_68 @cite_47 . User studies have shown that hierarchical approaches that collapse several nodes in larger meta-nodes can improve graph readability in cases of high edge density @cite_24 . The graph layout also has a significant impact on the readability of graphs @cite_8 . Some work has been done to adapt spectral and force-directed graph layouts @cite_61 to that recompute the position of nodes at time @math based on the previous positions at time @math - @math minimizing displacement of vertices @cite_66 @cite_63 @cite_54 @cite_72 or to propose new stress-minimization'' strategies to map the changes in the graph @cite_60 .
@cite_61 @cite_69 @cite_14 @cite_47 @cite_8 @cite_36 @cite_60 @cite_54 @cite_24 @cite_72 @cite_63 @cite_5 @cite_15 @cite_68 @cite_66
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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. 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. We present the H3 layout technique for drawing large directed graphs as node-link diagrams in 3D hyperbolic space. We can lay out much larger structures than can be handled using traditional techniques for drawing general graphs because we assume a hierarchical nature of the data. We impose a hierarchy on the graph by using domain-specific knowledge to find an appropriate spanning tree. Links which are not part of the spanning tree do not influence the layout but can be selectively drawn by user request. The volume of hyperbolic 3-space increases exponentially, as opposed to the familiar geometric increase of euclidean 3-space. We exploit this exponential amount of room by computing the layout according to the hyperbolic metric. We optimize the cone tree layout algorithm for 3D hyperbolic space by placing children on a hemisphere around the cone mouth instead of on its perimeter. Hyperbolic navigation affords a Focus+Context view of the structure with minimal visual clutter. We have successfully laid out hierarchies of over 20,000 nodes. Our implementation accommodates navigation through graphs too large to be rendered interactively by allowing the user to explicitly prune or expand subtrees. 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.