Drawing graphs by eigenvectors: theory and practice
نویسندگان
چکیده
منابع مشابه
Drawing Graphs by Eigenvectors: Theory and Practice
The spectral approach for graph visualization computes the layout of a graph using certain eigenvectors of related matrices. Some important advantages of this approach are an ability to compute optimal layouts (according to specific requirements) and a very rapid computation time. In this paper we explore spectral visualization techniques and study their properties from different points of view...
متن کاملDrawing Graphs by Eigenvectors: Theory and Practice*
K e y w o r d s G r a p h drawing, Laplaclan, Eigenvectors, Fledler vector, Force-directed layout, Spectral graph theory 1. I N T R O D U C T I O N A graph G(V, E) is an abstract structure that is used to model a relation E over a set V of entities. Graph drawing is a standard means for visualizing relational information, and its ultimate usefulness depends on the readability of the resulting l...
متن کاملACE: A Fast Multiscale Eigenvectors Computation for Drawing Huge Graphs
We present an extremely fast graph drawing algorithm for very large graphs, which we term ACE (for Algebraic multigrid Computation of Eigenvectors). ACE exhibits an improvement of something like two orders of magnitude over the fastest algorithms we are aware of; it draws graphs of millions of nodes in less than a minute. ACE finds an optimal drawing by minimizing a quadratic energy function. T...
متن کاملCharacterizing Graph Drawing with Eigenvectors
Two definitions of the problem of graph drawing are considered, and an analytical solution is provided for each of them. The solutions obtained make use of the eigenvectors of the Laplacian matrix of a related structure. The procedures give good results for symmetrical graphs, and they have already been used for drawing fullerene molecules in the literature. The analysis characterizes precisely...
متن کاملCharacterising Graph Drawing with Eigenvectors
We consider the problem of embedding a graph on n vertices in Euclidean space R for k n Typically k would be or By posing the problem as minimising the squared norm of the appropriately weighted distance be tween adjacent points subject to natural normalising conditions we arrive at a formulation of the problem for which the optimal solution can be sim ply computed in terms of the eigenvectors ...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2005
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2004.08.015