Conference Paper

A Space Efficient Clustered Visualization of Large Graphs

Univ. of Technol., Sydney
DOI: 10.1109/ICIG.2007.10 Conference: Image and Graphics, 2007. ICIG 2007. Fourth International Conference on
Source: IEEE Xplore


This paper proposes a new technique for visualizing large graphs of several ten thousands of vertices and edges. To achieve the graph abstraction, a hierarchical clustered graph is extracted from a general large graph based on the community structures which are discovered in the graph. An enclosure geometrical partitioning algorithm is then applied to achieve the space optimization. For graph drawing, we technically use the combination of a spring-embbeder algorithm and circular drawings that archives the goal of optimization of display space and aesthetical niceness. We also discuss an associated interaction mechanism accompanied with the layout solution. Our interaction not only allows users to navigate hierarchically up and down through the entire clustered graph, but also provides a way to navigate multiple clusters concurrently. Animation is also implemented to preserve users' mental maps during the interaction.

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    • "Since the ordering of our nodes is important, we prefer to see the user-highlighted node in the context of the entire tree as is. There are more space optimal ways to represent a tree than this (Nguyen and Huang, 2007), but the advantage of the radial view for our tree is that leaf nodes are adjacent to each other, and the nature of our clustering means that adjacent leaf nodes close together on the rim should have similar function. The algorithm for laying out the tree starts with the leaves. "
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    • "Balzer and Deussen [2] define a dynamic layout in order to show clustered graphs with animation. Huang and Nguyen [5] introduce an efficient layout scheme, scaling to thousands of nodes. Papadopoulos and Voglis [10] benefit from modular decomposition [3] in order to draw their graph. "
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    ABSTRACT: Graphs are abstract representations that can describe a large set of real world phenomena and that, possibly, scale to the order of hundreds of thousands of nodes and millions of edges. Benefiting from such graphs can be better performed by means of visual interaction. However, in the domain of large graphs, excessive processing and limited display space bound the possibilities for visual presentation and processing. In this line, we introduce GMine, a prototype system that uses an innovative data structure, the Graph-Tree. The engineering of GMine allows for scalability over huge graphs stored on disk, an extended graph representation embracing both hierarchical and plain organization, and the interactive browsing of graph hierarchies.
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    ABSTRACT: Current applications have produced graphs on the order of hundreds of thousands of nodes and millions of edges. To take advantage of such graphs, one must be able to find patterns, outliers and communities. These tasks are better performed in an interactive environment, where human expertise can guide the process. For large graphs, though, there are some challenges: the excessive processing requirements are prohibitive, and drawing hundred-thousand nodes results in cluttered images hard to comprehend. To cope with these problems, we propose an innovative framework suited for any kind of tree-like graph visual design. GMine integrates (a) a representation for graphs organized as hierarchies of partitions - the concepts of SuperGraph and Graph-Tree; and (b) a graph summarization methodology - CEPS. Our graph representation deals with the problem of tracing the connection aspects of a graph hierarchy with sublinear complexity, allowing one to grasp the neighborhood of a single node or of a group of nodes in a single click. Once a neighborhood is found, GMine provides interactive mining capabilities permitted by the summarization of its nodes through efficient algebraic processing. As a proof of concept, the visual environment of GMine is instantiated as a system in which large graphs can be investigated globally and locally.
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