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Results tagged with spectral-graph-theory
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user 4362
Questions related to the spectrum of graphs, defined using one of the possible variants of the discrete Laplace operator or Laplacian matrix. See https://en.wikipedia.org/wiki/Discrete_Laplace_operator
39
votes
6
answers
4k
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Is the Laplacian on a manifold the limit of graph Laplacians?
Here's the sort of thing I have in mind. Let $M$ be a Riemannian manifold, compact if it helps, and let $\Delta_M$ be the Laplace-Beltrami operator. Choose a sequence of triangulations of $M$ so tha …
- 29.2k
8
votes
2
answers
2k
views
Small eigenvalues and spectral clustering
Let $L$ be the discrete Laplacian associated to an undirected graph. It is well-known that the spectral gap of $L$, i.e. the smallest nonzero eigenvalue, is a measure of how well connected the graph …
- 29.2k
3
votes
1
answer
636
views
Cheeger inequality for the maximal eigenvalue
Let $G = (V,E)$ be an undirected graph and let $L = I - D^{-1/2} A D^{-1/2}$ be its normalized Laplacian matrix. The Cheeger inequality asserts that:
$$\frac{\Phi_G^2}{2} \leq \lambda_2 \leq 2 \Phi_G …
- 29.2k