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Results tagged with laplacian
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user 1266
The Laplacian matrix is the representation of a graph in matrix form.
3
votes
Graph Laplacian simple eigenvalues
(If the Laplacian eigenvalues of a graph are all simple, then so are the eigenvalues of its complement.) …
- 12.1k
3
votes
Boundaries of the eigenvalues of a symmetric matrix (or of its Lapacian)
Let $L(G)$ denote the Laplacian of $G$. Then $L(G)$ is positive semidefinite. …
- 12.1k
7
votes
Connectivity of weighted graph and zero Laplacian eigenvalues
Then $B\Delta B^T$ is your weighted Laplacian and, since $BB^T$ and $B\Delta B^T$ have the same rank, we're done. …
- 12.1k
17
votes
Accepted
Are these three different notions of a graph Laplacian?
These are usually known as the Laplacian, the normalized Laplacian and the unsigned Laplaian. All three are positive semidefinite. If the graph is regular, they all provide the same information. … The normalized Laplacian is the right tool for the analysis of random walks. …
- 12.1k