A stochastic complex network model
Author:
David J. Aldous
Journal:
Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 152-161
MSC (2000):
Primary 60K35; Secondary 05C80, 90B15, 94C15
DOI:
https://doi.org/10.1090/S1079-6762-03-00123-9
Published electronically:
December 18, 2003
MathSciNet review:
2029476
Full-text PDF Free Access
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Additional Information
Abstract: We introduce a stochastic model for complex networks possessing three qualitative features: power-law degree distributions, local clustering, and slowly growing diameter. The model is mathematically natural, permits a wide variety of explicit calculations, has the desired three qualitative features, and fits the complete range of degree scaling exponents and clustering parameters.
- Réka Albert and Albert-László Barabási, Statistical mechanics of complex networks, Rev. Modern Phys. 74 (2002), no. 1, 47–97. MR 1895096, DOI https://doi.org/10.1103/RevModPhys.74.47
me103 D.J. Aldous and A.G. Percus, Scaling and universality in continuous length combinatorial optimization, Proc. Natl. Acad. Sci. USA 100 (2003), 11211–11215.
me104 D.J. Aldous, A tractable complex network model based on the stochastic mean-field model of distance, arXiv:cond-mat/0304701, 2003.
me101 D.J. Aldous and J.M. Steele, The objective method: Probabilistic combinatorial optimization and local weak convergence, in Probability on Discrete Structures, H. Kesten (ed.), 1–72, Springer, 2003.
barabasi02 A.L. Barabási, Linked: the new science of networks, Perseus Press, Cambridge, MA, 2002.
boll-scale B. Bollobás and O. Riordan, Mathematical results on scale-free random graphs, Handbook of Graphs and Networks (S. Bornholdt and H.G. Schuster, eds.), Wiley, 2002.
buchanan02 M. Buchanan, Nexus: Small worlds and the groundbreaking science of networks, W.W. Norton, 2002.
DM02 S.N. Dorogovtsev and J.F.F. Mendes, Evolution of networks, Adv. Phys. 51 (2002), 1079–1187.
fabr02 A. Fabrikant, E. Koutsoupias, and C.H. Papadimitriou, Heuristically optimized trade-offs: a new paradigm for power laws in the internet, International Colloq. Automata, Languages and Programming, 2002.
- J. Jost and M. P. Joy, Spectral properties and synchronization in coupled map lattices, Phys. Rev. E (3) 65 (2002), no. 1, 016201, 9. MR 1877614, DOI https://doi.org/10.1103/PhysRevE.65.016201
menczer02 F. Menczer, Growing and navigating the small world web by local content, Proc. Natl. Acad. Sci. USA 99 (2002), 14014–14019.
MD03 J.F.F. Mendes and S.N. Dorogovtsev, Evolution of networks: From biological nets to the internet and WWW, Oxford Univ. Press, 2003.
newman-survey M.E.J. Newman, The structure and function of complex networks, SIAM Review 45 (2003), 167–256.
RBar03 E. Ravasz and A.L. Barabási, Hierarchical organization in complex networks, Physical Review E 67 (2003), 026112.
watts03 D.J. Watts, Six degrees: the science of a connected age, W.W. Norton, 2003.
yule24 G.U. Yule, A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, Philos. Trans. Roy. Soc. London Ser. B 213 (1924), 21–87.
AB02 R. Albert and A.-L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys. 74 (2002), 47–97.
me103 D.J. Aldous and A.G. Percus, Scaling and universality in continuous length combinatorial optimization, Proc. Natl. Acad. Sci. USA 100 (2003), 11211–11215.
me104 D.J. Aldous, A tractable complex network model based on the stochastic mean-field model of distance, arXiv:cond-mat/0304701, 2003.
me101 D.J. Aldous and J.M. Steele, The objective method: Probabilistic combinatorial optimization and local weak convergence, in Probability on Discrete Structures, H. Kesten (ed.), 1–72, Springer, 2003.
barabasi02 A.L. Barabási, Linked: the new science of networks, Perseus Press, Cambridge, MA, 2002.
boll-scale B. Bollobás and O. Riordan, Mathematical results on scale-free random graphs, Handbook of Graphs and Networks (S. Bornholdt and H.G. Schuster, eds.), Wiley, 2002.
buchanan02 M. Buchanan, Nexus: Small worlds and the groundbreaking science of networks, W.W. Norton, 2002.
DM02 S.N. Dorogovtsev and J.F.F. Mendes, Evolution of networks, Adv. Phys. 51 (2002), 1079–1187.
fabr02 A. Fabrikant, E. Koutsoupias, and C.H. Papadimitriou, Heuristically optimized trade-offs: a new paradigm for power laws in the internet, International Colloq. Automata, Languages and Programming, 2002.
JJ02 J. Jost and M.P. Joy, Evolving networks with distance preferences, Physical Review E 66 (2002), 036126.
menczer02 F. Menczer, Growing and navigating the small world web by local content, Proc. Natl. Acad. Sci. USA 99 (2002), 14014–14019.
MD03 J.F.F. Mendes and S.N. Dorogovtsev, Evolution of networks: From biological nets to the internet and WWW, Oxford Univ. Press, 2003.
newman-survey M.E.J. Newman, The structure and function of complex networks, SIAM Review 45 (2003), 167–256.
RBar03 E. Ravasz and A.L. Barabási, Hierarchical organization in complex networks, Physical Review E 67 (2003), 026112.
watts03 D.J. Watts, Six degrees: the science of a connected age, W.W. Norton, 2003.
yule24 G.U. Yule, A mathematical theory of evolution, based on the conclusions of Dr. J. C. Willis, Philos. Trans. Roy. Soc. London Ser. B 213 (1924), 21–87.
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Additional Information
David J. Aldous
Affiliation:
Department of Statistics, 367 Evans Hall, U.C. Berkeley, CA 94720
MR Author ID:
24555
Email:
aldous@stat.berkeley.edu
Keywords:
Complex network,
Poisson process,
PWIT,
random graph,
scale-free,
small worlds,
Yule process
Received by editor(s):
July 22, 2003
Published electronically:
December 18, 2003
Additional Notes:
The author was supported in part by NSF Grant DMS-0203062.
Communicated by:
Ronald L. Graham
Article copyright:
© Copyright 2003
American Mathematical Society
