Transport between multiple users in complex networks

European Physical Journal B

Volumn 57, Issue 2, 2007, Pages 165-174

  Carmi, S ^a   Wu, Z ^b   Lopez E ^c   Havlin, S ^a,b   Eugene Stanley, H ^b  

^a BAR ILAN UNIVERSITY   (Israel)

^b BOSTON UNIVERSITY   (United States)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX NETWORKS; NETWORK DEGREE DISTRIBUTIONS; SCALE FREE NETWORKS;

ELECTRIC CONDUCTANCE; ELECTRIC CONDUCTIVITY; ELECTRIC POWER TRANSMISSION; ELECTRIC RESISTANCE;

NETWORKS (CIRCUITS);

EID: 34250359141     PISSN: 14346028     EISSN: 14346036     Source Type: Journal    
DOI: 10.1140/epjb/e2007-00129-0     Document Type: Article

References (39)

1. S. Havlin, D. ben-Avraham, Adv. Phys. 36, 695 (1987)
2. D. ben-Avraham, S. Havlin, Diffusion and reactions in fractals and disordered systems (Cambridge, New York, 2000)
3. A. Bunde, S. Havlin, edited by Fractals and Disordered Systems (Springer, New York, 1996)
4. R. Albert, A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002);
5. R. Pastor-Satorras, A. Vespignani, Structure and Evolution of the Internet: A Statistical Physics Approach (Cambridge University Press, Cambridge, 2004);
6. S.N. Dorogovsetv, J.F.F. Mendes, Evolution of Networks: From Biological Nets to the Internet and WWW (Oxford University Press, Oxford, 2003)
7. G. Bonanno, G. Caldarelli, F. Lillo, R.N. Mantegna, Phys. Rev. E 68, 046130 (2003)
8. J.-P. Onnela, A. Chakraborti, K. Kaski, J. Kertész, A. Kanto, Phys. Rev. E 68, 056110 (2003)
9. H. Inaoka, T. Ninomiya, K. Taniguchi, T. Shimizu, H. Takayasu, Fractal Network derived from banking transaction - An analysis of network structures formed by financial institutions, Bank of Japan Working Paper Series, 04-E-04 (2004);
10. H. Inaoka, H. Takayasu, T. Shimizu, T. Ninomiya, K. Taniguchi, Physica, A 339, 62 (2004)
11. P. Erdös, A. Rényi, Publ. Math. (Debreccen) 6, 290 (1959)
12. B. Bollobás, Random Graphs (Academic Press, Orlando, 1985)
13. A.-L. Barabási, R. Albert, Science 286, 509 (1999)
14. P.L. Krapivsky, S. Redner, F. Leyvraz, Phys. Rev. Lett. 85, 4629 (2000)
15. H.A. Simon, Biometrika 42, 425 (1955)
16. R. Cohen, S. Havlin, Phys. Rev. Lett. 90, 058701 (2003)
17. SF(G)
18. E. López, S.V. Buldyrev, S. Havlin, H.E. Stanley, Phys. Rev. Lett. 94, 248701 (2005)
19. S. Havlin, E. López, S.V. Buldyrev, H.E. Stanley, in Diffusion Fundamentals, edited by Jörg Kärger, Farida Grinberg, Paul Heitjans (Leipzig: Universitätsverlag, 2005), pp. 38-48
20. E. Lopez, S. Carmi, S. Havlin, S. Buldyrev, H.E. Stanley, Physica D 224, 69 (2006)
21. G.R. Grimmett, H. Kesten, J. Lond. Math. Soc. 30, 171 (1984); e-print arXiv:math/0107068
22. D.-S. Lee, H. Rieger, Europhys. Lett. 73, 471 (2006)
23. Z. Toroczkai, K. Bassler, Nature 428, 716 (2004)
24. J.D. Noh, H. Rieger, Phys. Rev. Lett. 92, 118701 (2004)
25. V. Sood, S. Redner, D. ben-Avraham, J. Phys. A, 38, 109 (2005)
26. L.K. Gallos, Phys. Rev. E 70, 046116 (2004)
27. B. Tadic, G.J. Rodgers, Advances in Complex Systems 5, 445 (2002)
28. The dynamical properties we study are related to transport on networks and differ from those which treat the network topology itself as evolving in time [10,11]
29. R.K. Ahuja, T.L. Magnanti, J.B. Orlin, Network Flows: Theory, Algorithms, and Applications (Prentice Hall, 1993)
30. The study of community structure in social networks has led some authors (M.E.J. Newman, M. Girvan, Phys. Rev. E 69, 026113 (2004);
31. F. Wu, B.A. Huberman, Eur. Phys. J. B 38, 331 (2004)) to develop methods in which networks are considered as electrical networks in order to identify communities. In these studies, however, transport properties have not been addressed
32. M. Molloy, B. Reed, Random Struct. Algorithms 6, 161 (1995)
33. G. Kirchhoff, Ann. Phys. Chem. 72 497 (1847);
34. N. Balabanian, Electric Circuits (McGraw-Hill, New York, 1994)
35. S. Kirkpatrick, Proceedings of Inhomogeneous Superconductors Conference, Berkeley Springs, W. Va, edited by S.A. Wolf, D.U. Gubser, A.I.P. Conf. Procs. 58, 79 (1979)
36. B.V. Cherkassky, Algorithmica 19, 390 (1997)
37. Z. Wu, L.A. Braunstein, S. Havlin, H.E. Stanley, Phys. Rev. Lett. 96, 148702 (2006)
38. S. Carmi, S. Havlin, S. Kirkpatrick, Y. Shavitt, E. Shir, MEDUSA - New Model of Internet Topology Using k-shell Decomposition, arXiv: cond-mat/0601240
39. Y. Shavitt, E. Shir, ACM SIGCOMM Computer Communication Review, 35, 71 (2005)