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4 questions
2
votes
1
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Eigenvalues of directed Laplacian matrix $L$ and $DL$, where $D$ is a diagonal matrix with positive entries
I have a weighted Laplacian matrix $L$ of a strongly connected directed graph and a diagonal matrix $D$ with positive entries. Since the graph is directed, $L$ is non-symmetric real. Further, since ...
- 1,446
1
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0
answers
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What do you call this class of matrices with a unique positive eigenvalue associated to a graph?
I am looking for the name of a class of symmetric matrices $M\in\Bbb R^{n\times n}$ that I can associate to a (finite simple) graph $G=(V,E)$ with $V=\{1,...,n\}$ and that have the following ...
- 13.6k
5
votes
2
answers
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Lower bound for smallest eigenvalue of symmetric doubly-stochastic Metropolis-Hasting transition matrix
For my master's thesis research, I stumbled upon a question concerning the Metropolis-Hasting transition matrix $W$.
Context $\quad$
Let me start with some context. I consider connected undirected ...
- 51
1
vote
0
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158
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Interpreting (Fiedler) spectral bisectioning
I would appreciate help on how to interpret the results of spectral bisectioning of a graph.
Given a $G=(V,E)$ with size $N$ represented by $Q$ its Laplacian matrix where the eigenvalues are ordered ...
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