Peacock Bundles: Bundle Coloring for Graphs with Globality-Locality Trade-off

Bundling of graph edges (node-to-node connections) is a common technique to enhance visibility of overall trends in the edge structure of a large graph layout, and a large variety of bundling algorithms have been proposed. However, with strong bundling, it becomes hard to identify origins and destinations of individual edges. We propose a solution: we optimize edge coloring to differentiate bundled edges. We quantify strength of bundling in a flexible pairwise fashion between edges, and among bundled edges, we quantify how dissimilar their colors should be by dissimilarity of their origins and destinations. We solve the resulting nonlinear optimization, which is also interpretable as a novel dimensionality reduction task. In large graphs the necessary compromise is whether to differentiate colors sharply between locally occurring strongly bundled edges ("local bundles"), or also between the weakly bundled edges occurring globally over the graph ("global bundles"); we allow a user-set global-local tradeoff. We call the technique "peacock bundles". Experiments show the coloring clearly enhances comprehensibility of graph layouts with edge bundling.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016

Persistent Homology Guided Force-Directed Graph Layouts

Graphs are commonly used to encode relationships among entities, yet their abstractness makes them difficult to analyze. Node-link diagrams are popular for drawing graphs, and force-directed layouts provide a flexible method for node arrangements that use local relationships in an attempt to reveal the global shape of the graph. However, clutter and overlap of unrelated structures can lead to confusing graph visualizations. This paper leverages the persistent homology features of an undirected graph as derived information for interactive manipulation of force-directed layouts. We first discuss how to efficiently extract 0-dimensional persistent homology features from both weighted and unweighted undirected graphs. We then introduce the interactive persistence barcode used to manipulate the force-directed graph layout. In particular, the user adds and removes contracting and repulsing forces generated by the persistent homology features, eventually selecting the set of persistent homology features that most improve the layout. Finally, we demonstrate the utility of our approach across a variety of synthetic and real datasets

AmbiguityVis: Visualization of Ambiguity in Graph Layouts

Node-link diagrams provide an intuitive way to explore networks and have inspired a large number of automated graphlayout strategies that optimize aesthetic criteria. However, any particular drawing approach cannot fully satisfy all these criteriasimultaneously, producing drawings with visual ambiguities that can impede the understanding of network structure. To bring attentionto these potentially problematic areas present in the drawing, this paper presents a technique that highlights common types of visualambiguities: ambiguous spatial relationships between nodes and edges, visual overlap between community structures, and ambiguityin edge bundling and metanodes. Metrics, including newly proposed metrics for abnormal edge lengths, visual overlap in communitystructures and node/edge aggregation, are proposed to quantify areas of ambiguity in the drawing. These metrics and others arethen displayed using a heatmap-based visualization that provides visual feedback to developers of graph drawing and visualizationapproaches, allowing them to quickly identify misleading areas. The novel metrics and the heatmap-based visualization allow a userto explore ambiguities in graph layouts from multiple perspectives in order to make reasonable graph layout choices. The effectivenessof the technique is demonstrated through case studies and expert reviews