All Questions
9 questions
1
vote
0
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95
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Algorithm for efficiently calculating $(A+\sum_{i=1}^n B_i)^{-1}$ where $A^{-1}\in\mathbb S^n_+$ is known and $B_i$ are sparse matrices
Let $A\in\mathbb R^{n\times n}$ be a symmetric positive-definite matrix and $A^{-1}$ is already known. Now I want to compute the matrix $(A+\sum_{i=1}^n B_i)^{-1}$ where each $B_i$ is a sparse ...
- 601
2
votes
0
answers
514
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Normalized Laplacian matrix versus walk Laplacian matrix (or normalized adjacency matrix versus walk adjacency matrix)
In graphs, found that two different normalization matrices exist for Laplacian and adiacency matrix. I will ask about the adjacency matrix (for the Laplacian matrix the questions are the same). The ...
- 121
4
votes
2
answers
1k
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What's the full assumption for Laplacian matrix $L=BB^T=\Delta-A$?
Graph with no-selfloop, no-multi-edges, unweighted.
directed
For directed graph Adjacency matrix is a non-symmetric matrix $A_{in}$ considering indegree or $A_{out}$ considering outdegree. Degree ...
- 211
5
votes
1
answer
382
views
Is it possible to compute a valid Laplacian matrix from an effective resistance matrix?
I am wondering whether it is possible to retrieve a node-admittance matrix $G$ (also called Laplacian matrix) in a purely resistive network composed of nets $\{1, \dots, i, \dots, j, \dots, n\}$, from ...
10
votes
1
answer
600
views
is it possible to have two non-isomorphic non-regular graphs with the same adjacent spectrum and the same laplacian spectrum?
For two regular graphs $G$ and $H$, it is possible for them to share the same adjacent spectrum and the same laplacian spectrum. While, on the other hand, is it possible to have two non-regular graphs ...
- 103
3
votes
1
answer
247
views
If $A=BC$, where $A$ and $C$ are given Laplacian matrices, how to calculate $B$?
Let me be more specific: If $A=BC$, where $A$ and $C$ are given Laplacian matrices, how to calculate $B$? The graph corresponding to $A$ is a directed ring, which is strongly connected and $1_n$ and $...
- 143
4
votes
0
answers
374
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non-symmetric weak diagonal-dominant matrix, no decoupling: (a) is positive semi-definite? (b) has dim(ker)=1?
We are considering a matrix $A=(a_{ij})_{i,j=1,\ldots,d}\in\mathbb{R}^{d\times d}$ with the following property: $a_{ii}=-\sum_{j\neq i}a_{ij}$, i.e., the matrix is not only weak diagonal-dominant, but ...
- 329
1
vote
1
answer
647
views
If the two smallest eigenvalues of the Laplacian matrix of a network are equal to zero, then does it mean that the network is not connected? [closed]
What does it mean if the two smallest eigenvalues of the Laplacian matrix of a graph are equal to zero?
- 13
2
votes
0
answers
677
views
Bounds on smallest Eigenvalue of the Sum of a Standard Laplacian and a Diagonal Matrix
I'm trying to find upper boundaries on the smallest Eigenvalue $\lambda_1$ of $L + E$, where $L$ is a standard Laplacian of an unweighted digraph, with $\lambda_1(L) = 0$ and $E \in \{0,1\}^{n \times ...
- 21