Topic

# Graph drawing

About: Graph drawing is a research topic. Over the lifetime, 2941 publications have been published within this topic receiving 87084 citations. The topic is also known as: graph visualization.

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TL;DR: A modification of the spring‐embedder model of Eades for drawing undirected graphs with straight edges is presented, developed in analogy to forces in natural systems, for a simple, elegant, conceptually‐intuitive, and efficient algorithm.

Abstract: SUMMARY We present a modification of the spring-embedder model of Eades [ Congresses Numerantium, 42, 149–160, (1984)] for drawing undirected graphs with straight edges. Our heuristic strives for uniform edge lengths, and we develop it in analogy to forces in natural systems, for a simple, elegant, conceptuallyintuitive, and efficient algorithm.

5,242 citations

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TL;DR: The field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process high-dimensional data on graphs as discussed by the authors, which are the analogs to the classical frequency domain and highlight the importance of incorporating the irregular structures of graph data domains when processing signals on graphs.

Abstract: In applications such as social, energy, transportation, sensor, and neuronal networks, high-dimensional data naturally reside on the vertices of weighted graphs. The emerging field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process such signals on graphs. In this tutorial overview, we outline the main challenges of the area, discuss different ways to define graph spectral domains, which are the analogs to the classical frequency domain, and highlight the importance of incorporating the irregular structures of graph data domains when processing signals on graphs. We then review methods to generalize fundamental operations such as filtering, translation, modulation, dilation, and downsampling to the graph setting and survey the localized, multiscale transforms that have been proposed to efficiently extract information from high-dimensional data on graphs. We conclude with a brief discussion of open issues and possible extensions.

3,475 citations

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TL;DR: The University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications, is described and a new multilevel coarsening scheme is proposed to facilitate this task.

Abstract: We describe the University of Florida Sparse Matrix Collection, a large and actively growing set of sparse matrices that arise in real applications The Collection is widely used by the numerical linear algebra community for the development and performance evaluation of sparse matrix algorithms It allows for robust and repeatable experiments: robust because performance results with artificially generated matrices can be misleading, and repeatable because matrices are curated and made publicly available in many formats Its matrices cover a wide spectrum of domains, include those arising from problems with underlying 2D or 3D geometry (as structural engineering, computational fluid dynamics, model reduction, electromagnetics, semiconductor devices, thermodynamics, materials, acoustics, computer graphics/vision, robotics/kinematics, and other discretizations) and those that typically do not have such geometry (optimization, circuit simulation, economic and financial modeling, theoretical and quantum chemistry, chemical process simulation, mathematics and statistics, power networks, and other networks and graphs) We provide software for accessing and managing the Collection, from MATLAB™, Mathematica™, Fortran, and C, as well as an online search capability Graph visualization of the matrices is provided, and a new multilevel coarsening scheme is proposed to facilitate this task

3,456 citations

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TL;DR: This work has developed a graph-theoretical network visualization toolbox, called BrainNet Viewer, to illustrate human connectomes as ball-and-stick models, and helps researchers to visualize brain networks in an easy, flexible and quick manner.

Abstract: The human brain is a complex system whose topological organization can be represented using connectomics. Recent studies have shown that human connectomes can be constructed using various neuroimaging technologies and further characterized using sophisticated analytic strategies, such as graph theory. These methods reveal the intriguing topological architectures of human brain networks in healthy populations and explore the changes throughout normal development and aging and under various pathological conditions. However, given the huge complexity of this methodology, toolboxes for graph-based network visualization are still lacking. Here, using MATLAB with a graphical user interface (GUI), we developed a graph-theoretical network visualization toolbox, called BrainNet Viewer, to illustrate human connectomes as ball-and-stick models. Within this toolbox, several combinations of defined files with connectome information can be loaded to display different combinations of brain surface, nodes and edges. In addition, display properties, such as the color and size of network elements or the layout of the figure, can be adjusted within a comprehensive but easy-to-use settings panel. Moreover, BrainNet Viewer draws the brain surface, nodes and edges in sequence and displays brain networks in multiple views, as required by the user. The figure can be manipulated with certain interaction functions to display more detailed information. Furthermore, the figures can be exported as commonly used image file formats or demonstration video for further use. BrainNet Viewer helps researchers to visualize brain networks in an easy, flexible and quick manner, and this software is freely available on the NITRC website (www.nitrc.org/projects/bnv/).

3,048 citations

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2,703 citations