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A stochastic complex network model
Author(s):
David
J.
Aldous
Journal:
Electron. Res. Announc. Amer. Math. Soc.
9
(2003),
152-161.
MSC (2000):
Primary 60K35;
Secondary 05C80, 90B15, 94C15
Posted:
December 18, 2003
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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.
References:
-
- 1.
- R. Albert and A.-L. Barabási, Statistical mechanics of complex networks, Rev. Mod. Phys. 74 (2002), 47-97. MR 2003d:82055
- 2.
- D.J. Aldous and A.G. Percus, Scaling and universality in continuous length combinatorial optimization, Proc. Natl. Acad. Sci. USA 100 (2003), 11211-11215.
- 3.
- D.J. Aldous, A tractable complex network model based on the stochastic mean-field model of distance, arXiv:cond-mat/0304701, 2003.
- 4.
- 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.
- 5.
- A.L. Barabási, Linked: the new science of networks, Perseus Press, Cambridge, MA, 2002.
- 6.
- 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.
- 7.
- M. Buchanan, Nexus: Small worlds and the groundbreaking science of networks, W.W. Norton, 2002.
- 8.
- S.N. Dorogovtsev and J.F.F. Mendes, Evolution of networks, Adv. Phys. 51 (2002), 1079-1187.
- 9.
- 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.
- 10.
- J. Jost and M.P. Joy, Evolving networks with distance preferences, Physical Review E 66 (2002), 036126. MR 2002i:37133
- 11.
- F. Menczer, Growing and navigating the small world web by local content, Proc. Natl. Acad. Sci. USA 99 (2002), 14014-14019.
- 12.
- J.F.F. Mendes and S.N. Dorogovtsev, Evolution of networks: From biological nets to the internet and WWW, Oxford Univ. Press, 2003.
- 13.
- M.E.J. Newman, The structure and function of complex networks, SIAM Review 45 (2003), 167-256.
- 14.
- E. Ravasz and A.L. Barabási, Hierarchical organization in complex networks, Physical Review E 67 (2003), 026112.
- 15.
- D.J. Watts, Six degrees: the science of a connected age, W.W. Norton, 2003.
- 16.
- 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
Email:
aldous@stat.berkeley.edu
DOI:
10.1090/S1079-6762-03-00123-9
PII:
S 1079-6762(03)00123-9
Keywords:
Complex network,
Poisson process,
PWIT,
random graph,
scale-free,
small worlds,
Yule process
Received by editor(s):
July 22, 2003
Posted:
December 18, 2003
Additional Notes:
The author was supported in part by NSF Grant DMS-0203062.
Communicated by:
Ronald L. Graham
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