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66
A Multilevel Algorithm for ForceDirected GraphDrawing
, 2003
"... We describe a heuristic method for drawing graphs which uses a multilevel framework combined with a forcedirected placement algorithm. ..."
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Cited by 89 (3 self)
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We describe a heuristic method for drawing graphs which uses a multilevel framework combined with a forcedirected placement algorithm.
Network Visualization by Semantic Substrates
 IEEE Transactions on Visualization and Computer Graphics
"... Abstract—Networks have remained a challenge for information visualization designers because of the complex issues of node and link layout coupled with the rich set of tasks that users present. This paper offers a strategy based on two principles: (1) layouts are based on userdefined semantic substr ..."
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Cited by 60 (8 self)
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Abstract—Networks have remained a challenge for information visualization designers because of the complex issues of node and link layout coupled with the rich set of tasks that users present. This paper offers a strategy based on two principles: (1) layouts are based on userdefined semantic substrates, which are nonoverlapping regions in which node placement is based on node attributes, (2) users interactively adjust sliders to control link visibility to limit clutter and thus ensure comprehensibility of source and destination. Scalability is further facilitated by user control of which nodes are visible. We illustrate our semantic substrates approach as implemented in NVSS 1.0 with legal precedent data for up to 1122 court cases in three regions with 7645 legal citations. Index Terms — Network visualization, semantic substrate, information visualization, graphical user interfaces. 1
Managing Attack Graph Complexity through Visual Hierarchical Aggregation
 In VizSEC/DMSEC ’04: Proceedings of the 2004 ACM workshop on Visualization and
, 2004
"... We describe a framework for managing network attack graph complexity through interactive visualization, which includes hierarchical aggregation of graph elements. Aggregation collapses nonoverlapping subgraphs of the attack graph to single graph vertices, providing compression of attack graph compl ..."
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Cited by 39 (4 self)
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We describe a framework for managing network attack graph complexity through interactive visualization, which includes hierarchical aggregation of graph elements. Aggregation collapses nonoverlapping subgraphs of the attack graph to single graph vertices, providing compression of attack graph complexity. Our aggregation is recursive (nested), according to a predefined aggregation hierarchy. This hierarchy establishes rules at each level of aggregation, with the rules being based on either common attribute values of attack graph elements or attack graph connectedness. The higher levels of the aggregation hierarchy correspond to higher levels of abstraction, providing progressively summarized visual overviews of the attack graph. We describe rich visual representations that capture relationships among our semanticallyrelevant attack graph abstractions, and our views
A Multidimensional Approach to ForceDirected Layouts of Large Graphs
, 2000
"... Abstract. We present a novel hierarchical forcedirected method for drawing large graphs. The algorithm produces a graph embedding in an Euclidean space E of any dimension. A two or three dimensional drawing of the graph is then obtained by projecting a higherdimensional embedding into a two or thr ..."
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Cited by 36 (5 self)
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Abstract. We present a novel hierarchical forcedirected method for drawing large graphs. The algorithm produces a graph embedding in an Euclidean space E of any dimension. A two or three dimensional drawing of the graph is then obtained by projecting a higherdimensional embedding into a two or three dimensional subspace of E. Projecting highdimensional drawings onto two or three dimensions often results in drawings that are “smoother ” and more symmetric. Among the other notable features of our approach are the utilization of a maximal independent set filtration of the set of vertices of a graph, a fast energy function minimization strategy, efficient memory management, and an intelligent initial placement of vertices. Our implementation of the algorithm can draw graphs with tens of thousands of vertices using a negligible amount of memory in less than one minute on a midrange PC. 1
ASKGraphView: A Large Scale Graph Visualization System
 IEEE Transactions on Visualization and Computer Graphics
, 2006
"... Abstract—We describe ASKGraphView, a nodelinkbased graph visualization system that allows clustering and interactive navigation of large graphs, ranging in size up to 16 million edges. The system uses a scalable architecture and a series of increasingly sophisticated clustering algorithms to cons ..."
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Cited by 34 (0 self)
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Abstract—We describe ASKGraphView, a nodelinkbased graph visualization system that allows clustering and interactive navigation of large graphs, ranging in size up to 16 million edges. The system uses a scalable architecture and a series of increasingly sophisticated clustering algorithms to construct a hierarchy on an arbitrary, weighted undirected input graph. By lowering the interactivity requirements we can scale to substantially bigger graphs. The user is allowed to navigate this hierarchy in a top down manner by interactively expanding individual clusters. ASKGraphView also provides facilities for filtering and coloring, annotation and cluster labeling. Index Terms — Information Visualization, Graph Visualization, Graph Clustering. 1
MGV: A System for Visualizing Massive MultiDigraphs
 IEEE Transactions on Visualization and Computer Graphics
, 2002
"... We describe MGV, an integrated visualization and exploration system for massive multidigraph navigation. ..."
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Cited by 30 (7 self)
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We describe MGV, an integrated visualization and exploration system for massive multidigraph navigation.
A Fast MultiDimensional Algorithm for Drawing Large Graphs
 In Graph Drawing’00 Conference Proceedings
, 2000
"... We present a novel hierarchical forcedirected method for drawing large graphs. The algorithm produces a graph embedding in an Euclidean space E of any dimension. A two or three dimensional drawing of the graph is then obtained by projecting a higherdimensional embedding into a two or three dimensi ..."
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Cited by 28 (4 self)
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We present a novel hierarchical forcedirected method for drawing large graphs. The algorithm produces a graph embedding in an Euclidean space E of any dimension. A two or three dimensional drawing of the graph is then obtained by projecting a higherdimensional embedding into a two or three dimensional subspace of E. Projecting highdimensional drawings onto two or three dimensions often results in drawings that are "smoother" and more symmetric. Among the other notable features of our approach are the utilization of a maximal independent set filtration of the set of vertices of a graph, a fast energy function minimization strategy, e#cient memory management, and an intelligent initial placement of vertices. Our implementation of the algorithm can draw graphs with tens of thousands of vertices using a negligible amount of memory in less than one minute on a midrange PC. 1 Introduction Graphs are common in many applications, from data structures to networks, from software engineering...
Visualizing Related Metabolic Pathways in Two and a Half Dimensions
, 2003
"... We propose a method for visualizing a set of related metabolic pathways using 2 2 D graph drawing. Interdependent, twodimensional layouts of each pathway are stacked on top of each other so that biologists get a full picture of subtle and significant di#erences among the pathways. Layouts are ..."
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Cited by 26 (7 self)
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We propose a method for visualizing a set of related metabolic pathways using 2 2 D graph drawing. Interdependent, twodimensional layouts of each pathway are stacked on top of each other so that biologists get a full picture of subtle and significant di#erences among the pathways. Layouts are determined by a global layout of the union of all pathwayrepresenting graphs using a variant of the proven Sugiyama approach for layered graph drawing that allows edges to cross if they appear in di#erent graphs.
Algorithms for Drawing Clustered Graphs
, 1997
"... In the mid 1980s, graphics workstations became the main platforms for software and information engineers. Since then, visualization of relational information has become an essential element of software systems. Graphs are commonly used to model relational information. They are depicted on a graphics ..."
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Cited by 25 (2 self)
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In the mid 1980s, graphics workstations became the main platforms for software and information engineers. Since then, visualization of relational information has become an essential element of software systems. Graphs are commonly used to model relational information. They are depicted on a graphics workstation as graph drawings. The usefulness of the relational model depends on whether the graph drawings effectively convey the relational information to the users. This thesis is concerned with finding good drawings of graphs. As the amount of information that we want to visualize becomes larger and the relations become more complex, the classical graph model tends to be inadequate. Many extended models use a node hierarchy to help cope with the complexity. This thesis introduces a new graph model called the clustered graph. The central theme of the thesis is an investigation of efficient algorithms to produce good drawings for clustered graphs. Although the criteria for judging the qua...
Balanced Aspect Ratio Trees and Their Use for Drawing Very Large Graphs
 Journal of Graph Algorithms and Applications
, 1998
"... We describe a new approach for clusterbased drawing of large graphs, which obtains clusters by using binary space partition (BSP) trees. We also introduce a novel BSPtype decomposition, called the balanced aspect ratio (BAR) tree, which guarantees that the cells produced are convex and have bounde ..."
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Cited by 21 (10 self)
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We describe a new approach for clusterbased drawing of large graphs, which obtains clusters by using binary space partition (BSP) trees. We also introduce a novel BSPtype decomposition, called the balanced aspect ratio (BAR) tree, which guarantees that the cells produced are convex and have bounded aspect ratios. In addition, the tree depth is O(log n), and its construction takes O(n log n) time, where n is the number of points. We show that the BAR tree can be used to recursively divide a graph embedded in the plane into subgraphs of roughly equal size, such that the drawing of each subgraph has a balanced aspect ratio. As a result, we obtain a representation of a graph as a collection of O(log n) layers, where each succeeding layer represents the graph in an increasing level of detail. The overall running time of the algorithm is O(n log n+m+D0(G)), where n and m are the number of vertices and edges of the graph G, andD0(G) is the time it takes to obtain an initial embedding of G in the plane. In particular, if the graph is planar each layer is a graph drawn with straight lines and without crossings on the n×n grid and the running time reduces to O(n log n).