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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 97 (9 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
Graph drawing by stress majorization
 GRAPH DRAWING
, 2004
"... One of the most popular graph drawing methods is based of achieving graphtheoretic target ditsances. This method was used by Kamada and Kawai [15], who formulated it as an energy optimization problem. Their energy is known in the multidimensional scaling (MDS) community as the stress function. In th ..."
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Cited by 93 (12 self)
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One of the most popular graph drawing methods is based of achieving graphtheoretic target ditsances. This method was used by Kamada and Kawai [15], who formulated it as an energy optimization problem. Their energy is known in the multidimensional scaling (MDS) community as the stress function. In this work, we show how to draw graphs by stress majorization, adapting a technique known in the MDS community for more than two decades. It appears that majorization has advantages over the technique of Kamada and Kawai in running time and stability. We also present a few extensions to the basic energy model which can improve layout quality and computation speed in practice. Majorizationbased optimization is essential to these extensions.
ACE: A Fast Multiscale Eigenvector Computation for Drawing Huge Graphs
, 2002
"... We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE finds an optimal drawing by minimizing a quadratic energy function due to Hall, using a novel algebraic multigrid technique. The algorithm exhibits ..."
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Cited by 74 (13 self)
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We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE finds an optimal drawing by minimizing a quadratic energy function due to Hall, using a novel algebraic multigrid technique. The algorithm exhibits an improvement of something like two orders of magnitude over the fastest algorithms we are aware of; it draws graphs of a million nodes in less than a minute. Moreover, the algorithm can deal with more general entities, such as graphs with masses and negative weights (to be defined in the text), and it appears to be applicable outside of graph drawing too.
Graph Drawing by HighDimensional Embedding
 In GD02, LNCS
, 2002
"... We present a novel approach to the aesthetic drawing of undirected graphs. The method has two phases: first embed the graph in a very high dimension and then project it into the 2D plane using PCA. Experiments we have carried out show the ability of the method to draw graphs of 10 nodes in few seco ..."
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Cited by 71 (10 self)
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We present a novel approach to the aesthetic drawing of undirected graphs. The method has two phases: first embed the graph in a very high dimension and then project it into the 2D plane using PCA. Experiments we have carried out show the ability of the method to draw graphs of 10 nodes in few seconds. The new method appears to have several advantages over classical methods, including a significantly better running time, a useful inherent capability to exhibit the graph in various dimensions, and an effective means for interactive exploration of large graphs.
Drawing Graphs with NonUniform Vertices
, 2002
"... The vertices of most graphs that appear in real applications are nonuniform. They can be circles, ellipses, rectangles, or other geometric elements of varying shapes and sizes. Unfortunately, current force directed methods for laying out graphs are suitable mostly for graphs whose vertices are zero ..."
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Cited by 36 (4 self)
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The vertices of most graphs that appear in real applications are nonuniform. They can be circles, ellipses, rectangles, or other geometric elements of varying shapes and sizes. Unfortunately, current force directed methods for laying out graphs are suitable mostly for graphs whose vertices are zerosized and dimensionless points. It turns out that naively extending these methods to handle nonuniform vertices results in serious deficiencies in terms of output quality and performance. In this paper we try to remedy this situation by identifying the special characteristics and problematics of such graphs and offering several algorithms for tackling them. The algorithms can be viewed as carefully constructed extensions of forcedirected methods, and their output quality and performance are similar.
Drawing Huge Graphs by Algebraic Multigrid Optimization. Multiscale Modeling and Simulation
, 2003
"... Abstract. We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE exhibits a vast improvement over the fastest algorithms we are currently aware of; using a serial PC, it draws graphs of millions of node ..."
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Cited by 30 (3 self)
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Abstract. We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE exhibits a vast improvement over the fastest algorithms we are currently aware of; using a serial PC, it draws graphs of millions of nodes in less than a minute. ACE finds an optimal drawing by minimizing a quadratic energy function. The minimization problem is expressed as a generalized eigenvalue problem, which is solved rapidly using a novel algebraic multigrid technique. The same generalized eigenvalue problem seems to come up also in other fields, hence ACE appears to be applicable outside graph drawing too.
Network Visualization by Meaningful Substrates
"... 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 fivelayer hierarchy of network visualization situations with associated tasks: from simple node ..."
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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 fivelayer hierarchy of network visualization situations with associated tasks: from simple node and link situations to more elaborate situations involving node labels, directed links, node attributes, and link attributes. Then, it offers a strategy based on tying node placement to node attributes within nonoverlapping regions. These userdefined meaningful substrates enable users to easily see which links remain within a region or cross to other regions. Link visibility is controlled by check boxes so that selected subsets of links can be displayed. To further limit display clutter, users can set sliders to control which nodes within a region have their edges visible. We illustrate our meaningful substrate approach in a modest example with legal precedents for 49 cases with 368 precedents, and show these in our implementation of NVMS 1.0.
OneDimensional Graph Drawing: Part II — AxisbyAxis Stress Minimization
"... Abstract. Graph drawing algorithms based on minimizing the socalled stress energy strive to place nodes in accordance with target distances. Such algorithms were first introduced to the graph drawing field by Kamada and Kawai [11], and they had previously been used to visualize general kinds of dat ..."
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Abstract. Graph drawing algorithms based on minimizing the socalled stress energy strive to place nodes in accordance with target distances. Such algorithms were first introduced to the graph drawing field by Kamada and Kawai [11], and they had previously been used to visualize general kinds of data by multidimensional scaling. In this paper we suggest a novel algorithm for axisbyaxis minimization of the Stress energy. This algorithm is suitable for a onedimensional layout, where one axis of the drawing is already given and an additional axis needs to be computed. In general, the proposed algorithm produces aesthetically superior layouts compared to other 1D drawing algorithms. Moreover, our algorithm can be used for multidimensional graph drawing, where it has time and space complexity advantages compared with other stress minimization algorithms. 1