Edge Modification Criteria for Enhancing the Communicability of Digraphs
Abstract
We introduce new broadcast and receive communicability indices that can be used as global measures of how effectively information is spread in a directed network. Furthermore, we describe fast and effective criteria for the selection of edges to be added to (or deleted from) a given directed network so as to enhance these network communicability measures. Numerical experiments illustrate the effectiveness of the proposed techniques.
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References
1.
F. Arrigo and M. Benzi, Updating and downdating techniques for optimizing network communicability, SIAM J. Sci. Comput., 38 (2016), pp. B25--B49.
2.
M. Benzi, E. Estrada, and C. Klymko, Ranking hubs and authorities using matrix functions, Linear Algebra Appl., 438 (2013), pp. 2447--2474.
3.
M. Benzi and C. Klymko, Total communicability as a centrality measure, J. Complex Netw., 1 (2013), pp. 124--149.
4.
M. Benzi and C. Klymko, On the limiting behavior of parameter-dependent network centrality measures, SIAM J. Matrix Anal. Appl., 36 (2015), pp. 686--706.
5.
P. Bonacich Power and centrality: A family of measures, Amer. J. Sociol., 92 (1987), pp. 1170--1182.
6.
J. J. Crofts, E. Estrada, D. J. Higham, and A. Taylor, Mapping directed networks, Electron. Trans. Numer. Anal., 37 (2010), pp. 337--350.
7.
T. Davis and Y. Hu, University of Florida Sparse Matrix Collection, http://www.guettel.com/funm_kryl/.
8.
E. Estrada and N. Hatano, Statistical--mechanical approach to subgraph centrality in complex networks, Chem. Phys. Lett., 439 (2007), pp. 247--251.
9.
E. Estrada and N. Hatano, Communicability in complex networks, Phys. Rev. E, 77 (2008), 036111.
10.
E. Estrada, N. Hatano, and M. Benzi, The physics of communicability in complex networks, Phys. Rep., 514 (2012), pp. 89--119.
11.
E. Estrada and J. A. Rodríguez-Velázquez, Subgraph centrality in complex networks, Phys. Rev. E, 71 (2005), 056103.
12.
A. Farahat, T. Lofaro, J. C. Miller, G. Rae, and L. A. Ward, Authority rankings from HITS, PageRank, and SALSA: Existence, uniqueness, and effect of initialization, SIAM J. Sci. Comput., 27 (2006), pp. 1181--1201.
13.
M. C. Gates and M. E. J. Woolhouse, Controlling infectious disease through the targeted manipulation of contact network structure, Epidemics, 12 (2015), pp. 11--19.
14.
Gephi Sample Dataset, http://wiki.gephi.org/index.php/Datasets.
15.
G. H. Golub and G. Meurant, Matrices, Moments and Quadrature with Applications, Princeton University Press, Princeton, NJ, 2010.
16.
G. H. Golub and C. F. Van Loan, Matrix Computations, 4th ed., Johns Hopkins University Press, Baltimore, MD, 2013.
17.
S. Güttel, Toolbox for MATLAB, www.mathe.tu-freiberg.de/$\sim$guttels/funm_kryl/.
18.
J. B. Hawkins and A. Ben--Israel, On generalized matrix functions, Linear Multilinear Algebra, 1 (1973), pp. 163--171.
19.
N. J. Higham, Functions of Matrices. Theory and Computation, SIAM, Philadelphia, 2008.
20.
S. Hoory, N. Linial, and A. Wigderson, Expander graphs and their applications, Bull. Amer. Math. Soc., 43 (2006), pp. 439--561.
21.
R. A. Horn and C. R. Johnson, Matrix Analysis, 2nd ed., Cambridge University Press, Cambridge, 2013.
22.
J. Kleinberg, Authoritative sources in a hyperlinked environment, J. ACM, 46 (1999), pp. 604--632.
23.
A. N. Langville and C. D. Meyer, Google's PageRank and Beyond: The Science of Search Engine Rankings, Princeton University Press, Princeton, NJ, 2006.
24.
H. Tong, B. Aditya Prakash, T. Eliassi--Rad, M. Faloutsos, and C. Faloutsos, Gelling, and melting, large graphs by edge manipulation, in Proceedings of the 21st ACM International Conference on Information and Knowledge Management, 2012, pp. 245--254.
25.
P. Tsapras, Dataset for experiments on link analysis ranking algorithms, http://www.cs.toronto.edu/ tsap/experiments/datasets/index.html.
26.
J. Wu, M. Barahona, Y. Tan, and H. Deng, Natural connectivity of complex networks, Chinese Phys. Lett., 27 (2010), 078902.
27.
J. Wu, M. Barahona, Y. Tan, and H. Deng, Robustness of random graphs based on graph spectra, Chaos, 22 (2012), 043101.
28.
A. Zeng, L. Lü, and T. Zhou, Manipulating directed networks for better synchronization, New J. Phys., 14 (2012), 083006.
Information & Authors
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Published In
SIAM Journal on Matrix Analysis and Applications
Pages: 443 - 468
DOI: 10.1137/15M1034131
ISSN (online): 1095-7162
Copyright
© 2016, Society for Industrial and Applied Mathematics.
History
Submitted: 6 August 2015
Accepted: 13 January 2016
Published online: 31 March 2016
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