Dynamic graph exploration by interactively linked node-link diagrams and matrix visualizations

The visualization of dynamic graphs is a challenging task owing to the various properties of the underlying relational data and the additional time-varying property. For sparse and small graphs, the most efficient approach to such visualization is node-link diagrams, whereas for dense graphs with attached data, adjacency matrices might be the better choice. Because graphs can contain both properties, being globally sparse and locally dense, a combination of several visual metaphors as well as static and dynamic visualizations is beneficial. In this paper, a visually and algorithmically scalable approach that provides views and perspectives on graphs as interactively linked node-link and adjacency matrix visualizations is described. As the novelty of this technique, insights such as clusters or anomalies from one or several combined views can be used to influence the layout or reordering of the other views. Moreover, the importance of nodes and node groups can be detected, computed, and visualized by considering several layout and reordering properties in combination as well as different edge properties for the same set of nodes. As an additional feature set, an automatic identification of groups, clusters, and outliers is provided over time, and based on the visual outcome of the node-link and matrix visualizations, the repertoire of the supported layout and matrix reordering techniques is extended, and more interaction techniques are provided when considering the dynamics of the graph data. Finally, a small user experiment was conducted to investigate the usability of the proposed approach. The usefulness of the proposed tool is illustrated by applying it to a graph dataset, such as e co-authorships, co-citations, and a Comprehensible Perl Archive Network distribution.

Keyword-Based Knowledge Graph Exploration Based on Quadratic Group Steiner Trees

Exploring complex structured knowledge graphs (KGs) is challenging for non-experts as it requires knowledge of query languages and the underlying structure of the KGs. Keyword-based exploration is a convenient paradigm, and computing a group Steiner tree (GST) as an answer is a popular implementation. Recent studies suggested improving the cohesiveness of an answer where entities have small semantic distances from each other. However, how to efficiently compute such an answer is open. In this paper, to model cohesiveness in a generalized way, the quadratic group Steiner tree problem (QGSTP) is formulated where the cost function extends GST with quadratic terms representing semantic distances. For QGSTP we design a branch-and-bound best-first (B3F) algorithm where we exploit combinatorial methods to estimate lower bounds for costs. This exact algorithm shows practical performance on medium-sized KGs.