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On The Eigenvalue Distribution Of Adjacency Matrices For Connected Planar Graphs Cover

On The Eigenvalue Distribution Of Adjacency Matrices For Connected Planar Graphs

Open Access
|Dec 2015

References

  1. Adler M., van Moerbeke P., 2001. Hermitian, symmetric and symplectic random ensembles: PDEs for the distribution of the spectrum. Annals of Mathematics 153: 149–189.10.2307/2661373
  2. Barry R., Pace R., 1999. Monte Carlo estimates of the log determinant of large sparse matrices. Linear Algebra and Its Applications 289: 41–54.10.1016/S0024-3795(97)10009-X
  3. Box G., Jenkins G., 1976. Time series analysis: Forecasting, and control. Holden Day, San Francisco.
  4. Brouwer A., Haemers W., 2012. Spectra of graphs. Springer, New York.10.1007/978-1-4614-1939-6
  5. Cao D., Yuan H., 1993. Graphs characterized by the second eigenvalue. Journal of Graph Theory 17: 25–331.10.1002/jgt.3190170307
  6. Cao D., Yuan H., 1995. The distribution of eigenvalues of graphs. Linear Algebra and its Applications 216: 211–224.10.1016/0024-3795(93)00135-M
  7. Chung F., 1997. Spectral graph theory. American Mathematical Society, Providence, RI.
  8. Chung F., Lu L., Vu V., 2003. Spectra of random graphs with given expected degrees. Proceedings of the National Academy of Sciences 100: 6313–6318.10.1073/pnas.093749010016444312743375
  9. Cressie N., 1993. Statistics for spatial data. Wiley, New York.10.1002/9781119115151
  10. Faloutsos M., Faloutsos P., Faloutsos C., 1999. On power-law relationships of the internet topology. ACM SIGCOM Computer Communication Review 29: 251–262.10.1145/316194.316229
  11. Farrell P., Ehsanes Saleh A., Zhang Z., 2011. Methods of moments estimation in finite mixtures. Sankhyā: The Indian Journal of Statistics 73-A, Part 2: 218–230.10.1007/s13171-011-0011-3
  12. Fefferman C., Phong D., 1980. On the asymptotic eigenvalue distribution of a pseudo-differential operation. Proceedings of the National Academy of Sciences 77: 5622–5625.10.1073/pnas.77.10.562235012016592889
  13. Golub G., van der Vorst H., 2000. Numerical progress in eigenvalue computation in the 20th century. J. of Computational and Applied Mathematics 123: 35–65.10.1016/S0377-0427(00)00413-1
  14. Griffith D., 2000. Eigenfunction properties and approximations of selected incidence matrices employed in spatial analyses. Linear Algebra and its Applications 321: 95–112.10.1016/S0024-3795(00)00031-8
  15. Griffith D., 2003. Spatial autocorrelation and spatial filtering: Gaining understanding through theory and scientific visualization. Springer, New York.10.1007/978-3-540-24806-4_4
  16. Griffith D., 2004. Extreme eigenfunctions of adjacency matrices for planar graphs employed in spatial analyses. Linear Algebra and Its Applications 388: 201–219.10.1016/S0024-3795(03)00368-9
  17. Griffith D., Luhanga U., 2011. Approximating the inertia of the adjacency matrix of a connected planar graph that is the dual of a geographic surface partitioning. Geographical Analysis 43: 383–402.10.1111/j.1538-4632.2011.00828.x
  18. Hams A., de Raedt H., 2000. Fast algorithm for finding the eigenvalue distribution of very large matrices. Physical review, E: Statistical physics, plasmas, fluids, and related interdisciplinary topics 62 (#3): 4365–4377.10.1103/PhysRevE.62.4365
  19. Henson J., Reise S., Kim K., 2007. Detecting mixtures from structural model differences using latent variable mixture modeling: A comparison of relative model fit statistics. Structural Equation Modeling 14 (2): 202–226.10.1080/10705510709336744
  20. Huffer F., Wu H., 1998. Markov chain Monte Carlo for autologistic regression models with application to the distribution of plant species. Biometrics 54: 509–524.10.2307/3109759
  21. Hyndman J., Kostenko A., 2007. Minimum sample size requirements for seasonal forecasting models. Foresight 6: 12–15.
  22. Khorunzhy O., Shcherbina M., Vengerovsky V., 2004. Eigenvalue distribution of large weighted random graphs. Journal of Mathematical Physics 45 (#4): 1648–1672.10.1063/1.1667610
  23. Liu B., Bo Z., 2000. On the third largest eigenvalue of a graph. Linear Algebra and its Applications 317: 193–200.10.1016/S0024-3795(00)00159-2
  24. Martin R., Griffith D., 1998. Fast methods for fitting one-parameter spatial models. Department of Geography, Syracuse University Syracuse, NY (unpublished paper).
  25. Sylvester J., 1852. A demonstration of the theorem that every homogeneous quadratic polynomial is reducible by real orthogonal substitutions to the form of a sum of positive and negative squares. Philosophical Magazine Series 4, 4 (23): 138–142.10.1080/14786445208647087
  26. Tse R., 1997. An application of the ARIMA model to real estate prices in Hong Kong. Journal of Property Finance 8: 152–163.10.1108/09588689710167843
  27. Yong X., 1999. On the distribution of eigenvalues of a simple undirected graph. Linear Algebra and its Applications 295: 73–80.10.1016/S0024-3795(99)00077-4
DOI: https://doi.org/10.1515/quageo-2015-0035 | Journal eISSN: 2081-6383 | Journal ISSN: 2082-2103
Language: English
Page range: 39 - 60
Submitted on: Feb 2, 2015
Published on: Dec 30, 2015
Published by: Adam Mickiewicz University
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Related subjects:

© 2015 Daniel A. Griffith, published by Adam Mickiewicz University
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.