Approximations of the generalized inverse of the graph laplacian matrix

Internet Mathematics

Volumn 8, Issue 4, 2012, Pages 456-481

  Bozzo, Enrico ^a   Franceschet, Massimo ^a  

^a UNIVERSITY OF UDINE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84885441359     PISSN: 15427951     EISSN: None     Source Type: Journal    
DOI: 10.1080/15427951.2012.715115     Document Type: Article

References (30)

1. A. V. Aho, J. E. Hopcroft, and J. D. Ullman. The Design and Analysis of Computer Algorithms. Addison-Wesley, 1974.
2. E. Anderson, Z. Bai, C. Bischof, S. Blackford, Demmel J, J. Dongarra, et al. LAPACK Users Guide, 3rd edition. SIAM, 1999.
3. A.-L. Barabási and R. Albert. “Emergence of Scaling in Random Networks.” Science 286 (1999), 509–512.
4. A.-L. Barabási, R. Albert, and H. Jeong. “Mean-Field Theory for Scale-Free Random Networks.” Physica A 272:1-2 (1999), 173–187.
5. A. Ben-Israel and T. N. Greville. Generalized Inverses. Theory and Applications, 2nd edition. Springer, 2003.
6. L. Bergamaschi and M. Putti. “Numerical Comparison of Iterative Eigensolvers for Large Sparse Symmetric Positive Definite Matrices.” Computer Methods in Applied Mechanics and Engineering 191:45 (2002), 5233–5247.
7. B. Bollobás, O. Riordan, J. Spencer, and G. Tusnády. “The Degree Sequence of a Scale-Free Random Graph Process.” Random Structures and Algorithms 18:3 (2001), 279–290.
8. S. P. Borgatti. “Centrality and Network Flow.” Social Networks 27:1 (2005) 55–71.
9. U. Brandes and T. Erlebach, editors. Network Analysis: Methodological Foundations, Lecture Notes in Computer Science 3418. Springer, 2005.
10. U. Brandes and D. Fleischer. “Centrality Measures Based on Current Flow.” In Proc. 22nd Symp. Theoretical Aspects of Computer Science (STACS’05), pp. 533–544. Springer, 2005.
11. D. de Solla Price. “A General Theory of Bibliometric and Other Cumulative Advantage Processes.” Journal of the American Society for Information Science 27 (1976), 292–306.
12. P. Erdős and A. Rényi. “On the Evolution of Random Graphs.” Publications of the Mathematical Institute of the Hungarian Academy of Sciences 5 (1960), 17–61.
13. L. C. Freeman. “Centrality in Networks: I. Conceptual Clarification.” Social Networks 1 (1979), 215–239.
14. A. Ghosh, S. Boyd, and A. Saberi. “Minimizing Effective Resistance of a Graph.” SIAM Review 50:1 (2008), 37–66.
15. G. H. Golub and G. Meurant. Matrices, Moments and Quadrature with Applications, Princeton Series in Applied Mathematics. Princeton University Press, 2010.
16. G. H. Golub and C. F. Van Loan. Matrix Computations, 3rd edition. The Johns Hopkins University Press, 1996.
17. Y. Hu and J. A. Scott. “HSL MC73: A fast Multilevel Fiedler and Profile Reduction Code.” Tech. Rep. RAL-TR-2003-036, Rutherford Appleton Laboratory, 2003.
18. D. J. Klein and M. Randić. “Resistance Distance.” Journal of Mathematical Chemistry 12:1 (1993), 81–95.
19. R. B. Lehoucq, D. C. Sorensen, and C. Yang. ARPACK Users Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM, 1998.
20. D. Lusseau and M. E. J. Newman. “Identifying the Role That Animals Play in Their Social Networks.” Proceedings of the Royal Society B: Biological Sciences 271 (2004), S477–S481.
21. M. Newman. “A Measure of Betweenness Centrality Based on Random Walks.” Social Networks 27:1 (2005), 39–54.
22. M. E. J. Newman. Networks: An Introduction. Oxford University Press, 2010.
23. M. E. J. Newman, A.-L. Barabási, and D. J. Watts. The Structure and Dynamics of Networks. Princeton University Press, 2006.
24. R. Raz. “On the Complexity of Matrix Product.” SIAM Journal on Computing 32:5 (2003), 1356–1369.
25. Y. Saad. Iterative Methods for Sparse Linear Systems, 2nd edition. Society for Industrial and Applied Mathematics, 2003.
26. G. Sabidussi. “The Centrality Index of a Graph.” Psychometrika 31 (1966), 581–603.
27. H. A. Simon. “On a Class of Skew Distribution Functions.” Biometrika 42 (1955), 425–440.
28. R. Solomonoff and A. Rapoport. “Connectivity of Random Nets.” Bulletin of Mathematical Biophysics 13 (1951), 107–117.
29. K. Stephenson and M. Zelen. “Rethinking Centrality: Methods and Examples.” Social Networks 11:1 (1989), 1–37.
30. C. Zhan, G. Chen, and L. F. Yeung. “On the Distributions of Laplacian Eigenvalues versus Node Degrees in Complex Networks.” Physica A: Statistical Mechanics and Its Applications 389:8 (2010), 1779–1788.