Abstract.
The robustness of a communication scheme in a complex network may depend on the location of distinguished nodes. We collect different approaches to the idea of vulnerability and we give methods that help us to decide the good spots for the leader nodes. More specifically, we present a constructive method that yields the best location in a communication scheme for a leader node in the case that the underlying network is tree-shaped and show how it can be used for more general networks. In order to do that we consider a local approach via the bottleneck tree associated to a given node, as well as a uniform a approach by means of the so-called bottleneck network for several communication topologies.
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References
K. Burrage, Parallel and Sequential Methods for Ordinary Differential Equations (Numerical Mathematics and Scientific Computation) (Oxford University Press, 1997)
R. Albert, A.L. Barabási, Rev. Mod. Phys. 74, 47 (2002)
Y. Bar-Yam, Dynamics of Complex Systems (Addison-Wesley, 1997)
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 424, 175 (2006)
R. Cohen, K. Erez, D. Ben-Avraham, S. Havril, Phys. Rev. Lett. 85, 4626 (2000)
R. Cohen, K. Erez, D. Ben-Avraham, S. Havril, Phys. Rev. Lett. 86, 3682 (2001)
R. Criado, J. Flores, B. Hernández-Bermejo, J. Pello, M. Romance, J. Math. Mod. Algor. 4, 307 (2005)
R. Criado, A.G. del Amo, B. Hernández-Bermejo, M. Romance, J. Comput. App. Math. 192, 59 (2006)
P. Crucitti, V. Latora, M. Marchiori, A. Rapisarda, Physica A 320, 622 (2003)
A. H. Dekker, B.D. Colbert, Proceedings of ACSC04, the 27th Australasian Computer Science (Cairns, Australia, 2004), p. 685
P. Holme, J.-H. Kim, Phys. Rev. E 65, 066109 (2002)
V. Latora, M. Marchiori, Phys. Rev. Lett. 87, 198701 (2001)
V. Latora, M. Marchiori, Chaos, Solit. Fract. 20, 69 (2004)
M.E.J. Newman, M. Girvan, Phys. Rev. E. 69 026113 (2004)
C. Boyd, A. Mathuria, Protocols for Authentication and Key Establishment (Information Security and Cryptography) (Springer, 2003)
R. Criado, J. Flores, M.I. Gonzalez-Vasco, J. Pello, J. Comput. Appl. Math. (to appear)
M.E.J. Newman, SIAM Rev. 45, 167 (2003)
S.H. Strogatz, Nature 410, 268 (2001)
J.M. Bohli, M.I. González-Vasco, R. Steinwandt (preprint)
R. Albert, H. Jeong, A.L. Barabási, Nature 406, 378 (2000)
B. Bollobas, O. Riordan, Internet Math. 1, 1 (2003)
D.S. Callaway, M.E.J. Newman, S.H. Strogatz, D.J. Watts, Phys. Rev. Lett. 85, 5468 (2000)
S. Bornholdt, H.G. Schuster, From the Genome to the Internet (Wiley-VCH, Germany, 2003)
J.-H. Kim, K.-I. Goh, B. Kahng, D. Kim, Phys. Rev. Lett. 91, 058701 (2003)
V. Latora, M. Marchiori, Phys. Rev. E 71, 015103 (2005)
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Criado, R., Flores, J., Pello, J. et al. Optimal communication schemes in a complex network: From trees to bottleneck networks. Eur. Phys. J. Spec. Top. 146, 145–154 (2007). https://doi.org/10.1140/epjst/e2007-00175-x
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DOI: https://doi.org/10.1140/epjst/e2007-00175-x