Open Access
Issue
ESAIM: M2AN
Volume 58, Number 1, January-February 2024
Page(s) 131 - 155
DOI https://doi.org/10.1051/m2an/2023102
Published online 31 January 2024
  1. A.H. Al-Mohy and N.J. Higham, Computing the action of the matrix exponential, with an application to exponential integrators. SIAM J. Sci. Comput. 33 (2011) 488–511. [CrossRef] [MathSciNet] [Google Scholar]
  2. H. Alqahtani and L. Reichel, Multiple orthogonal polynomials applied to matrix function evaluation. BIT Numer. Math. 58 (2018) 835–849. [CrossRef] [Google Scholar]
  3. F. Arrigo and M. Benzi, Updating and downdating techniques for optimizing network communicability. SIAM J. Sci. Comput. 38 (2016) B25–B49. [CrossRef] [Google Scholar]
  4. V. Batagelj and A. Mrvar, Pajek datasets collection. http://vlado.fmf.uni-lj.si/pub/networks/data/ (2006). [Google Scholar]
  5. B. Beckermann, D. Kressner and M. Schweitzer, Low-rank updates of matrix functions. SIAM J. Matrix Anal. Appl. 39 (2018) 539–565. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Bellalij, L. Reichel, G. Rodriguez and H. Sadok, Bounding matrix functionals via partial global block lanczos decomposition. Appl. Numer. Math. 94 (2015) 127–139. [CrossRef] [MathSciNet] [Google Scholar]
  7. R.H. Byrd, M.E. Hribar and J. Nocedal, An interior point algorithm for large-scale nonlinear programming. SIAM J. Optim. 9 (1999) 877–900. [CrossRef] [MathSciNet] [Google Scholar]
  8. R.H. Byrd, J.C. Gilbert and J. Nocedal, A trust region method based on interior point techniques for nonlinear programming. Math. Program. 89 (2000) 149–185. [CrossRef] [MathSciNet] [Google Scholar]
  9. H. Chan and L. Akoglu, Optimizing network robustness by edge rewiring: a general framework. Data Min. Knowl. Discov. 30 (2016) 1395–1425. [CrossRef] [MathSciNet] [Google Scholar]
  10. H. Chan, L. Akoglu and H. Tong, Make it or break it: Manipulating robustness in large networks. In Proceedings of the 2014 SIAM International Conference on Data Mining. SIAM (2014) 325–333. [Google Scholar]
  11. T. Chen, A. Greenbaum, C. Musco and C. Musco, Error bounds for lanczos-based matrix function approximation. SIAM J. Matrix Anal. Appl. 43 (2022) 787–811. [CrossRef] [MathSciNet] [Google Scholar]
  12. F. Chung, F.R. Chung, F.C. Graham and L. Lu, Complex Graphs and Networks. American Mathematical Soc., Number 107 (2006). [CrossRef] [Google Scholar]
  13. S. Cipolla, F. Durastante and F. Tudisco, Nonlocal pagerank. ESAIM Math. Model. Numer. Anal. 55 (2021) 77–97. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  14. ComplexNetTSP PowerGrids, Highvoltage power grid networks. https://github.com/ComplexNetTSP/Power_grids/tree/v1.0.0 (2023). [Google Scholar]
  15. A. Cortinovis, D. Kressner and S. Massei, Divide-and-conquer methods for functions of matrices with banded or hierarchical low-rank structure. SIAM J. Matrix Anal. Appl. 43 (2022) 151–177. [CrossRef] [MathSciNet] [Google Scholar]
  16. P. Crescenzi, G. D’angelo, L. Severini and Y. Velaj, Greedily improving our own closeness centrality in a network. ACM Trans. Knowl. Discov. Data (TKDD) 11 (2016) 1–32. [Google Scholar]
  17. G. D’Angelo, M. Olsen and L. Severini, Coverage centrality maximization in undirected networks. In Vol. 43 Proceedings of the AAAI Conference on Artificial Intelligence (2019) 501–508. [Google Scholar]
  18. O. De la Cruz Cabrera, J. Jin, S. Noschese and L. Reichel, Communication in complex networks. Appl. Numer. Math. 172 (2022) 186–205. [CrossRef] [MathSciNet] [Google Scholar]
  19. E. Estrada, Virtual identification of essential proteins within the protein interaction network of yeast. Proteomics 6 (2006) 35–40. [CrossRef] [PubMed] [Google Scholar]
  20. E. Estrada and N. Hatano, Statistical-mechanical approach to subgraph centrality in complex networks. Chem. Phys. Lett. 439 (2007) 247–251. [CrossRef] [Google Scholar]
  21. E. Estrada and Ö. Bodin, Using network centrality measures to manage landscape connectivity. Ecol. Appl. 18 (2008) 1810–1825. [CrossRef] [PubMed] [Google Scholar]
  22. E. Estrada and N. Hatano, Communicability in complex networks. Phys. Rev. E 77 (2008) 036111. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  23. E. Estrada and N. Hatano, Returnability in complex directed networks (digraphs). Linear Algebra Appl. 430 (2009) 1886–1896. [CrossRef] [MathSciNet] [Google Scholar]
  24. E. Estrada and D.J. Higham, Network properties revealed through matrix functions. SIAM Rev. 52 (2010) 696–714. [CrossRef] [MathSciNet] [Google Scholar]
  25. E. Estrada and P.A. Knight, A First Course in Network Theory. Oxford University Press, USA (2015). [Google Scholar]
  26. C. Fenu, D. Martin, L. Reichel and G. Rodriguez, Block Gauss and anti-Gauss quadrature with application to networks. SIAM J. Matrix Anal. Appl. 34 (2013) 1655–1684. [CrossRef] [MathSciNet] [Google Scholar]
  27. P. Fika and M. Mitrouli, Aitken’s method for estimating bilinear forms arising in applications. Calcolo 54 (2017) 455–470. [CrossRef] [MathSciNet] [Google Scholar]
  28. T.N. for Research Core Team, https://github.com/bstabler/TransportationNetworks (2023). [Google Scholar]
  29. A. Frommer, K. Lund and D.B. Szyld, Block krylov subspace methods for functions of matrices. Electron. Trans. Numer. Anal. 47 (2017) 100–126. [MathSciNet] [Google Scholar]
  30. K. Garimella, G. De Francisci Morales, A. Gionis and M. Mathioudakis, Reducing controversy by connecting opposing views. In Proceedings of the Tenth ACM International Conference on Web Search and Data Mining. ACM (2017) 81–90. [Google Scholar]
  31. A. Ghosh and S. Boyd, Growing well-connected graphs. In Proceedings of the 45th IEEE Conference on Decision and Control. IEEE (2006) 6605–6611. [Google Scholar]
  32. A. Ghosh, S. Boyd and A. Saberi, Minimizing effective resistance of a graph. SIAM Rev. 50 (2008) 37–66. [CrossRef] [MathSciNet] [Google Scholar]
  33. D.F. Gleich, Pagerank beyond the web. SIAM Rev. 57 (2015) 321–363. [CrossRef] [MathSciNet] [Google Scholar]
  34. P. Grindrod and T. Lee, Comparison of social structures within cities of very different sizes. R. Soc. Open Sci. 3 (2016) 150526. [CrossRef] [Google Scholar]
  35. M.H. Gutknecht, Block Krylov space methods for linear systems with multiple right-hand sides: An introduction, edited by A.H. Siddiqi, I.S. Duff and O. Christensen. In Modern Mathematical Models, Methods and Algorithms for Real World Systems. New Delhi, Anamaya (2007) 420–447. [Google Scholar]
  36. N. Hale, N.J. Higham and L.N. Trefethen, Computing Aα, log(A), and related matrix functions by contour integrals. SIAM J. Numer. Anal. 46 (2008) 2505–2523. [CrossRef] [MathSciNet] [Google Scholar]
  37. P. Kandolf, A. Koskela, S.D. Relton and M. Schweitzer, Computing low-rank approximations of the Fréchet derivative of a matrix function using Krylov subspace methods. Numer. Linear Algebra Appl. 28 (2021) e2401. [CrossRef] [Google Scholar]
  38. D. Kressner, A Krylov subspace method for the approximation of bivariate matrix functions. In Structured Matrices in Numerical Linear Algebra, Vol. 30 of Springer INdAM Series. Springer, Cham (2019) 197–214. [CrossRef] [Google Scholar]
  39. L.T. Le, T. Eliassi-Rad and H. Tong, Met: A fast algorithm for minimizing propagation in large graphs with small eigen-gaps. In Proceedings of the 2015 SIAM International Conference on Data Mining. SIAM (2015) 694–702. [Google Scholar]
  40. U. Luxburg, A. Radl and M. Hein, Getting lost in space: Large sample analysis of the resistance distance. Adv. Neural Inf. Process. Syst. 23 (2010). [Google Scholar]
  41. S. Massei and F. Tudisco, Matlab code for “Optimizing network robustness via Krylov subspaces”. https://github.com/COMPiLELab/krylov_robustness (2023). [Google Scholar]
  42. R. Mathias, A chain rule for matrix functions and applications. SIAM J. Matrix Anal. Appl. 17 (1996) 610–620. [CrossRef] [MathSciNet] [Google Scholar]
  43. S. Medya, A. Silva, A. Singh, P. Basu and A. Swami, Group centrality maximization via network design. In Proceedings of the 2018 SIAM International Conference on Data Mining. SIAM (2018) 126–134. [Google Scholar]
  44. R.A. Meyer, C. Musco, C. Musco and D.P. Woodruff, Hutch++: optimal stochastic trace estimation. In Symposium on Simplicity in Algorithms (SOSA). Society for Industrial and Applied Mathematics (SIAM) Philadelphia, PA (2021) 142–155. [CrossRef] [Google Scholar]
  45. V. Nicosia, R. Criado, M. Romance, G. Russo and V. Latora, Controlling centrality in complex networks. Sci. Rep. 2 (2012) 218. [CrossRef] [Google Scholar]
  46. J. Nocedal and S.J. Wright, Numerical Optimization. Springer (1999). [CrossRef] [Google Scholar]
  47. S. Pozza and F. Tudisco, On the stability of network indices defined by means of matrix functions. SIAM J. Matrix Anal. Appl. 39 (2018) 1521–1546. [CrossRef] [MathSciNet] [Google Scholar]
  48. S. Saha, A. Adiga, B.A. Prakash and A.K.S. Vullikanti, Approximation algorithms for reducing the spectral radius to control epidemic spread. InProceedings of the 2015 SIAM International Conference on Data Mining. SIAM (2015) 568–576. [Google Scholar]
  49. M. Schweitzer, Sensitivity of matrix function based network communicability measures: Computational methods and a priori bounds. Preprint: arXiv:2303.01339 (2023). [Google Scholar]
  50. S.N.A.P. (SNAP), sparse networks collection. http://snap.stanford.edu/data/index.html (2023). [Google Scholar]
  51. H. Tong, B.A. 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. ACM (2012) 245–254. [Google Scholar]
  52. F. Tudisco and D.J. Higham, Node and edge nonlinear eigenvector centrality for hypergraphs. Commun. Phys. 4 (2021) 201. [CrossRef] [Google Scholar]
  53. P. Van Mieghem, D. Stevanović, F. Kuipers, C. Li, R. Van De Bovenkamp, D. Liu and H. Wang, Decreasing the spectral radius of a graph by link removals. Phys. Rev. E 84 (2011) 016101. [CrossRef] [PubMed] [Google Scholar]
  54. S. Vigna, Spectral ranking. Netw. Sci. 4 (2016) 433–445. [CrossRef] [Google Scholar]
  55. S. Wasserman and K. Faust, Social Network Analysis: Methods and Applications (1994). [CrossRef] [Google Scholar]
  56. Z. Yu, C. Wang, J. Bu, X. Wang, Y. Wu and C. Chen, Friend recommendation with content spread enhancement in social networks. Inf. Sci. 309 (2015) 102–118. [CrossRef] [Google Scholar]
  57. Y. Zhang, A. Adiga, A. Vullikanti and B.A. Prakash, Controlling propagation at group scale on networks. In 2015 IEEE International Conference on Data Mining. IEEE (2015) 619–628. [Google Scholar]

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