On Total Unimodularity of Edge–Edge Adjacency Matrices

Algorithmica ◽  
2013 ◽  
Vol 67 (2) ◽  
pp. 277-292 ◽  
Author(s):  
Yusuke Matsumoto ◽  
Naoyuki Kamiyama ◽  
Keiko Imai
Keyword(s):  
Total Unimodularity ◽  
Adjacency Matrices

scholarly journals Quantum walks defined by digraphs and generalized Hermitian adjacency matrices

2021 ◽  
Vol 20 (3) ◽  
Author(s):  
Sho Kubota ◽  
Etsuo Segawa ◽  
Tetsuji Taniguchi
Keyword(s):  
Quantum Walks ◽  
Adjacency Matrices

scholarly journals Iterative Methods for the Computation of the Perron Vector of Adjacency Matrices

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1522
Author(s):  
Anna Concas ◽  
Lothar Reichel ◽  
Giuseppe Rodriguez ◽  
Yunzi Zhang
Keyword(s):  
Iterative Methods ◽  
Adjacency Matrix ◽  
Lanczos Method ◽  
Power Method ◽  
Arnoldi Method ◽  
Multiple Eigenvalues ◽  
Computer Storage ◽  
Adjacency Matrices ◽  
Lanczos Methods ◽  
Perron Vector

The power method is commonly applied to compute the Perron vector of large adjacency matrices. Blondel et al. [SIAM Rev. 46, 2004] investigated its performance when the adjacency matrix has multiple eigenvalues of the same magnitude. It is well known that the Lanczos method typically requires fewer iterations than the power method to determine eigenvectors with the desired accuracy. However, the Lanczos method demands more computer storage, which may make it impractical to apply to very large problems. The present paper adapts the analysis by Blondel et al. to the Lanczos and restarted Lanczos methods. The restarted methods are found to yield fast convergence and to require less computer storage than the Lanczos method. Computed examples illustrate the theory presented. Applications of the Arnoldi method are also discussed.

scholarly journals Optimizing quadratic forms of adjacency matrices of trees and related eigenvalue problems

2001 ◽  
Vol 325 (1-3) ◽  
pp. 191-207
Author(s):  
Wai-Shun Cheung ◽  
Chi-Kwong Li ◽  
D.D. Olesky ◽  
P. van den Driessche
Keyword(s):  
Quadratic Forms ◽  
Eigenvalue Problems ◽  
Adjacency Matrices

Adjacency matrices of polarity graphs and of other C 4-free graphs of large size

2010 ◽  
Vol 55 (2-3) ◽  
pp. 221-233 ◽  
Author(s):  
M. Abreu ◽  
C. Balbuena ◽  
D. Labbate
Keyword(s):  
Large Size ◽  
Adjacency Matrices

Improved hidden clique detection by optimal linear fusion of multiple adjacency matrices

2015 ◽  
Author(s):  
Himanshu Nayar ◽  
Benjamin A. Miller ◽  
Kelly Geyer ◽  
Rajmonda S. Caceres ◽  
Steven T. Smith ◽  
...  
Keyword(s):  
Adjacency Matrices ◽  
Optimal Linear

scholarly journals Cayley digraphs with normal adjacency matrices

2009 ◽  
Vol 309 (13) ◽  
pp. 4343-4348 ◽  
Author(s):  
David S. Lyubshin ◽  
Sergey V. Savchenko
Keyword(s):  
Adjacency Matrices

scholarly journals Gap sets for the spectra of cubic graphs

2021 ◽  
Vol 1 (1) ◽  
pp. 1-38
Author(s):  
Alicia Kollár ◽  
Peter Sarnak
Keyword(s):  
Line Graphs ◽  
Cubic Graphs ◽  
Content Type ◽  
Ramanujan Graphs ◽  
Adjacency Matrices

We study gaps in the spectra of the adjacency matrices of large finite cubic graphs. It is known that the gap intervals ( 2 2 , 3 ) (2 \sqrt {2},3) and [ − 3 , − 2 ) [-3,-2) achieved in cubic Ramanujan graphs and line graphs are maximal. We give constraints on spectra in [ − 3 , 3 ] [-3,3] which are maximally gapped and construct examples which achieve these bounds. These graphs yield new instances of maximally gapped intervals. We also show that every point in [ − 3 , 3 ) [-3,3) can be gapped by planar cubic graphs. Our results show that the study of spectra of cubic, and even planar cubic, graphs is subtle and very rich.

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