Abstract.
Dynamical processes taking place on real networks define on them evolving subnetworks whose topology is not necessarily the same of the underlying one. We investigate the problem of determining the emerging degree distribution, focusing on a class of tree-like processes, such as those used to explore the Internet's topology. A general theory based on mean-field arguments is proposed, both for single-source and multiple-source cases, and applied to the specific example of the traceroute exploration of networks. Our results provide a qualitative improvement in the understanding of dynamical sampling and of the interplay between dynamics and topology in large networks like the Internet.
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References
Handbook of Graphs and Networks: From the Genome to the Internet, edited by S. Bornholdt, H.G. Schuster (Wiley-VCH, Berlin, 2002)
S.N. Dorogovtsev, J.F.F. Mendes, Evolution of networks: From biological nets to the Internet and WWW (Oxford University Press, Oxford, 2003)
R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002)
M.E.J. Newman, SIAM Rev. 45, 167 (2003)
S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, D.-U. Hwang, Phys. Rep. 424, 175 (2006)
T. Petermann, P. De Los Rios, Eur. Phys. J. B 38, 201 (2004)
M.P.H. Stumpf, C. Wiuf, R.M. May, PNAS 102, 4221 (2005); M.P.H. Stumpf, C. Wiuf, Phys. Rev. E 72, 036118 (2005)
A. Clauset, C. Moore, Phys. Rev. Lett. 94, 018701 (2005)
S.H. Lee, P.-J. Kim, H. Jeong, Phys. Rev. E 73, 016102 (2006)
L. Dall'Asta, J.I. Alvarez-Hamelin, A. Barrat, A. Vázquez, A. Vespignani, Phys. Rev. E 71, 036135 (2005); L. Dall'Asta, J.I. Alvarez-Hamelin, A. Barrat, A. Vázquez, A. Vespignani, Lect. Notes in Comp. Sci. 3405, 140 (2005); L. Dall'Asta, J.I. Alvarez-Hamelin, A. Barrat, A. Vázquez, A. Vespignani, Theor. Comp. Sci. 355, 6 (2006)
R. Pastor-Satorras, A. Vespignani, Evolution and structure on the Internet: a statistical physics approach (Cambridge University Press, Cambridge, 2004)
D. Achlioptas, A. Clauset, D. Kempe, C. Moore, in STOC'05, 694 (2005)
R. Cohen, M. Gonen, A. Wool, preprint arXiv:cs.NI/0611157 (2006)
R. Castro, M. Coates, G. Liang, R. Nowak, B. Yu, Statistical Science 19, 499 (2004)
T. Kalisky, R. Cohen, O. Mokryn, D. Dolev, Y. Shavitt, S. Havlin, Phys. Rev. E 74, 066108 (2006)
G. Pant, P. Srinivasan, F. Menczer, Web Dynamics edited by M. Levene and A. Poulovassilis (Springer, 2004)
R.M. Anderson, R.M. May, Infectious Diseases of Humans: Dynamics and Control (Oxford Univ. Press, Oxford, 1991)
Y. Moreno, M. Nekovee, A.F. Pacheco, Phys. Rev. E 69, 066130 (2004); M. Nekovee, Y. Moreno, G. Bianconi, M. Marsili, Physica A 374, 457 (2007)
E. Rogers, The diffusion of innovations (Free Press, New York, 1995). T.W. Valente, Network Models of the Diffusion of Innovations (Hampton Press, Cresskill, NJ, 1995)
M. Granovetter, Amer. J. Soc. 83, 1420 (1978)
M.E.J. Newman, Phys. Rev. E 66, 016128 (2002)
M. Boguñá, R. Pastor-Satorras, Phys. Rev. E 66, 047104 (2002)
N.C. Wormald, Ann. Appl. Probab. 5, 1217 (1995); N.C. Wormald, in Lectures on Approximation and Randomized Algorithms, edited by M. Karonski, H.J. Proemel, (Warsaw, 1999), pp. 73–155
M. Molloy, B. Reed, Comb., Prob. and Comp. 7, 295 (1998)
D. Achlioptas, Y. Peres, J. Amer. Math. Soc. 17, 947 (2004)
See e.g. the recent preprint, R. Oliveira, B. Zhang, and L. Zhang, “Observing the Evolution of Internet AS Topology”, to appear in ACM SIGCOMM, Kyoto, Japan (2007)
J. Pansiot, D. Grad, ACM Computer Communication Review 28, 41 (1998)
R. Govindan, H. Tangmunarunkit, IEEE INFOCOM 2000, 1371 (2000)
M. Faloutsos, P. Faloutsos, C. Faloutsos, Comput. Commun. Rev. 29, 251 (1999)
A. Lakhina, J. Byers, M. Crovella, P. Xie, Proc. IEEE INFOCOM 2003 (2003)
J.-L. Guillaume, M. Latapy, Complex Systems 16, 83 (2005); J.-L. Guillaume, M. Latapy, D. Magoni, Computer Networks 50, 3197 (2006)
Y. Shavitt, E. Shir, cs.NI/0504107
F. Viger, A. Barrat, L. Dall'Asta, C. Zhang, E. Kolaczyk, Phys. Rev. E 75, 056111 (2007)
A.D. Flaxman, J. Vera, preprint, arXiv:cond-mat/0705.3243 (2007)
F. Wu, B.A. Huberman, L.A. Adamic, J.R. Tyler, Physica A 337, 327 (2004)
W.O. Kermack, A.G. McKendrick, Proc. Roy. Soc. Lond. A 115, 700 (1927)
Y. Moreno, R. Pastor-Satorras, A. Vespignani, Eur. Phys. J. B 26, 521 (2002)
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Dall'Asta, L. Dynamic exploration of networks: from general principles to the traceroute process. Eur. Phys. J. B 60, 123–133 (2007). https://doi.org/10.1140/epjb/e2007-00326-9
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DOI: https://doi.org/10.1140/epjb/e2007-00326-9