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Why $x^{T}B^TWBx=\|W^{1/2}Bx\|^2_2$ for diagonal matrix W?

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#linear-algebra #matrices #positive-semidefinite #graph-laplacian
75
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Why $x^TLx = \sum_{(u,v)\in E} w_{uv}(x(u)-x(v))^2$ for Laplacian L?

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#linear-algebra #matrices #matrix-equations #laplacian #graph-laplacian
49
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I'd like to learn about constructing a graph Laplacian, reading material?

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#matrices #graph-theory #reference-request #graph-laplacian
101
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Graph Laplacian appellation

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#graph-theory #laplacian #spectral-graph-theory #graph-laplacian
164
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When/How An Undirected Graph Can Be Recovered From Graph Laplacian

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#matrices #graph-theory #positive-definite #symmetric-matrices #graph-laplacian
144
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Characterization of Graph Laplacians

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#matrices #graph-theory #positive-semidefinite #graph-laplacian
1.8k
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Trying to understand relationship between Dirichlet energy of graphs and discrete laplacian

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#spectral-graph-theory #graph-laplacian
57
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On the eigenvalue of the normalized graph Laplacian

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#graph-theory #eigenvalues-eigenvectors #graph-laplacian
1.2k
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Questions related to Laplacian matrix of a Graph

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#graph-theory #graph-laplacian #graph-connectivity
631
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Geometric multiplicity of $0$ in graph Laplacians

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#linear-algebra #matrices #eigenvalues-eigenvectors #spectral-graph-theory #graph-laplacian
28
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Take a graph $G$, and identify two vertices to create a contracted graph. Can we bound the graph laplacian of the new graph in terms of the old?

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#probability-theory #graph-theory #graph-laplacian
200
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Eigenvector of a complete graph Laplacian

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#matrices #eigenvalues-eigenvectors #graph-laplacian
82
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Shouldn't heat kernel on a weighted graph be inverse proportional to the shortest path length?

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#geometry #heat-equation #graph-laplacian
190
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Uniqueness of the solution of a linear system involving the graph Laplacian

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#linear-algebra #matrices #graph-theory #pseudoinverse #graph-laplacian
123
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Exponentiating similar Laplacians

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#linear-algebra #matrices #graph-theory #matrix-exponential #graph-laplacian

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