منابع مشابه
Spectral Partitioning with Multiple Eigenvectors
The gvuph partitioning problem is to divide the vertices of a graph into disjoint clusters to minimize the total cost of the edges cut by the clusters. A spectral partitioning heuristic uses the graph’s eigenvectors to construct a geometric representation of the graph (e.g., linear orderings) which are subsequently partitioned. Our main result shows that when all the eigenvectors are used, grap...
متن کاملLaplacian graph eigenvectors
If G is a graph, its Laplacian is the difference of the diagonal matrix of its vertex degrees and its adjacency matrix. The main thrust of the present article is to prove several Laplacian eigenvector “principles” which in certain cases can be used to deduce the effect on the spectrum of contracting, adding or deleting edges and/or of coalescing vertices. One application is the construction of ...
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 کاملSpectral partitioning with blends of eigenvectors
Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More generally, we provide pointwise convergence guarantees so that blends (linear combinations) of eigenvectors can be employed to solve data analysis problems with co...
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: Linear Algebra and its Applications
سال: 1988
ISSN: 0024-3795
DOI: 10.1016/0024-3795(88)90147-4