This paper presents a technique for visualizing the differences between two graphs. The technique assumes that a unique labeling of the nodes for each graph is available, where if a pair of labels match, they correspond to the same node in both graphs. Such labeling often exists in many application areas: IP addresses in computer networks, namespaces, class names, and function names in software engineering, to name a few. As many areas of the graph may be the same in both graphs, we visualize large areas of difference through a graph hierarchy. We introduce a path-preserving coarsening technique for degree one nodes of the same classification. We also introduce a path-preserving coarsening technique based on betweenness centrality that is able to illustrate major differences between two graphs.

The analysis of large graphs plays a prominent role in various fields of research and is relevant in many important application areas. Effective visual analysis of graphs requires appropriate visual presentations in combination with respective user interaction facilities and algorithmic graph analysis methods. How to design appropriate graph analysis systems depends on many factors, including the type of graph describing the data, the analytical task at hand, and the applicability of graph analysis methods. The most recent surveys of graph visualization and navigation techniques were presented by Herman et al. [HMM00] and Diaz [DPS02]. The first work surveyed the main techniques for visualization of hierarchies and graphs in general that had been introduced until 2000. The second work concentrated on graph layouts introduced until 2002. Recently, new techniques have been developed covering a broader range of graph types, such as time-varying graphs. Also, in accordance with ever growing amounts of graph-structured data becoming available, the inclusion of algorithmic graph analysis and interaction techniques becomes increasingly important. In this State-of-the-Art Report, we survey available techniques for the visual analysis of large graphs. Our review firstly considers graph visualization techniques according to the type of graphs supported. The visualization techniques form the basis for the presentation of interaction approaches suitable for visual graph exploration. As an important component of visual graph analysis, we discuss various graph algorithmic aspects useful for the different stages of the visual graph analysis process.

Many graph visualization systems use graph hierarchies to organize a large input graph into logical components. These approaches detect features globally in the data and place these features inside levels of a hierarchy. However, this feature detection is a global process and does not consider nodes of the graph near a feature of interest. TugGraph is a system for exploring paths and proximity around nodes and subgraphs in a graph. The approach modifies a pre-existing hierarchy in order to see how a node or subgraph of interest extends out into the larger graph. It is guaranteed to create path-preserving hierarchies, so that the abstraction shown is meaningful with respect to the structure of the graph. The system works well on graphs of hundreds of thousands of nodes and millions of edges. TugGraph is able to present views of this proximal information in the context of the entire graph in seconds, and does not require a layout of the full graph as input.

Network analysis is an important task in a wide variety of application domains including analysis of social, financial, or transportation networks, to name a few. The appropriate visualization of graphs may reveal useful insight into relationships between network entities and subnetworks. However, often further algorithmic analysis of network structures is needed. In this paper, we propose a system for effective visual analysis of graphs which supports multiple analytic tasks. Our system enhances any graph layout algorithm by an analysis stage which detects predefined or arbitrarily specified subgraph structures (motifs). These motifs in turn are used to filter or aggregate the given network, which is particularly useful for search and analysis of interesting structures in large graphs. Our approach is fully interactive and can be iteratively refined, supporting analysis of graph structures at multiple levels of abstraction. Furthermore, our system supports the analysis of data- or user-driven graph dynamics by showing the implications of graph changes on the identified subgraph structures. The interactive facilities may be flexibly combined for gaining deep insight into the network structures for a wide range of analysis tasks. While we focus on directed, weighted graphs, the proposed tools can be easily extended to undirected and unweighted graphs. The usefulness of our approach is demonstrated by application on a phone call data set [18]. 1

We present a new approach aimed at understanding the structure of connections in edge-bundling layouts. We combine the advantages of edge bundles with a bundle-centric simplified visual representation of a graph’s structure. For this, we first compute a hierarchical edge clustering of a given graph layout which groups similar edges together. Next, we render clusters at a user-selected level of detail using a new image-based technique that combines distance-based splatting and shape skeletonization. The overall result displays a given graph as a small set of overlapping shaded edge bundles. Luminance, saturation, hue, and shading encode edge density, edge types, and edge similarity. Finally, we add brushing and a new type of semantic lens to help navigation where local structures overlap. We illustrate the proposed method on several real-world graph datasets. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Picture/Image Generation—Line and curve generation I.3.5 [Computer Graphics]: Picture/Image Generation—Computational Geometry and Object Modeling 1.

Graph visualization systems often exploit opaque metanodes to reduce visual clutter and improve the readability of large graphs. This filtering can be done in a path-preserving way based on attribute values associated with the nodes of the graph. Despite the extensive use these representations, as far as we know, no formal experimentation exists to evaluate if they improve the readability of graphs. In this paper, we present the results of a user study that formally evaluates how such representations affect the readability of graphs. We also explore the effect of graph size and connectivity in terms of this primary research question. Overall, for our tasks, we did not find a significant difference when this clustering is used. However, if the graph is highly connected, these clusterings can improve performance. Also, if the graph is large enough and can be simplified into a few metanodes, benefits in performance on global tasks are realized. Under these same conditions, however, performance of local attribute tasks may be reduced. Categories and Subject Descriptors (according to ACM CCS): H.1.2 [Information Systems]: User/Machine Systems—Human Factors; G.2.2 [Discrete Mathematics]: Graph Theory—Graph Algorithms 1.

As users analyze data, visualization is important for both generating insight during exploration and displaying information for presentation purposes. While visualization systems have been very successful at the latter, their full potential as an aid for data exploration has yet to be realized. Existing systems have often focused on techniques for displaying information, requiring data to conform to specific file formats or allowing very limited manipulation of the data. In addition, most systems that provide a stronger link between data and visualization sacrifice the freedom of arbitrary composition. In this paper, we present DEFOG, a system that aims to more tightly integrate data exploration and visualization. DEFOG was designed to manipulate objects and as such, it is able to handle a wide range of data types. In addition, it allows flexible data manipulation through both visual and programmatic operations, all integrated in the same environment. By allowing both objects and their relationships to be displayed and combined, DEFOG provides great freedom for visual composition. To that end, it combines information visualization with infrastructure to support a variety of data including in-memory objects and operations found in vector-based graphics editors like select, move, scale, group, and copy-and-paste. We show that this system provides a natural way to use and combine data visualization techniques to explore a variety of data types, and present case studies that demonstrate its use in analyzing collections of workflow specifications and biochemical pathways. DEFOG: A System for Data-Backed Visual Composition

c t i v it y e p o r t 2009 Table of contents 1. Team.................................................................................... 1

Abstract: Tulip is an information visualization framework dedicated to the analysis and visualization of relational data. Based on a decade of research and development of this framework, we present the architecture, consisting of a suite of tools and techniques, that can be used to address a large variety of domain-specific problems. With Tulip, we aim to provide the developer with a complete library, supporting the design of interactive information visualization applications for relational data that can be tailored to the problems he or she is addressing. The current framework enables the development of algorithms, visual encodings, interaction techniques, data models, and domain-specific visualizations. The software model facilitates the reuse of components and allows the developers to focus on programming their application. This development pipeline makes the framework efficient for research prototyping as well as the development of end-user applications. Key-words: Graph visualization framework, scalable graph visualization, information visualization,

A graph consists of a set and a binary relation on that set. Each element of the set is a node of the graph, while each element of the binary relation is an edge of the graph that encodes a relationship between two nodes. Graph are pervasive in many areas of science, engineering, and the social sciences: servers on the Internet are connected, proteins interact in large biological systems, social networks encode the relationships between people, and functions call each other in a program. In these domains, the graphs can become very large, consisting of hundreds of thousands of nodes and millions of edges. Graph drawing approaches endeavour to place these nodes in two or three-dimensional space with the intention of fostering an understanding of the binary relation by a human being examining the image. However, many of these approaches to drawing do not exploit higher-level structures in the graph beyond the nodes and edges. Frequently, these structures can be exploited for drawing. As an example, consider a large computer network where nodes are servers and edges are connections between those servers. If a user would like understand how servers at UBC connect to the rest of the network, a drawing that accentuates the set of nodes representing those servers may be more helpful than an approach where all nodes are drawn in the same way. In a feature-based approach, features are subgraphs exploited for the purposes of drawing. We endeavour to depict not only the binary relation, but the high-level relationships between features. This thesis extensively explores a feature-based approach to graph visualization and demonstrates the viability of tools that aid in the visualization of large graphs. Our contributions lie in presenting and evaluating novel techniques and algorithms for graph visualization. We implement five systems in order to empirically evaluate these techniques and algorithms, comparing them to previous approaches. iii