Abstract
We investigate the effect of a specific edge weighting scheme ~(k i k j )β on distributed flow efficiency and robustness to cascading failures in scale-free networks. In particular, we analyze a simple, yet fundamental distributed flow model: current flow in random resistor networks. By the tuning of control parameter β and by considering two general cases of relative node processing capabilities as well as the effect of bandwidth, we explore the dependence of transport efficiency upon the correlations between the topology and weights. By studying the severity of cascades for different control parameter β, we find that network resilience to cascading overloads and network throughput is optimal for the same value of β over the range of node capacities and available bandwidth.
Similar content being viewed by others
References
R. Guimerà, A. Díaz-Guilera, F. Vega-Redondo, A. Cabrales, A. Arenas, Phys. Rev. Lett. 89, 248701 (2002)
G. Yan, T. Zhou, B. Hu, Z.Q. Fu, B.H. Wang, Phys. Rev. E 73, 046108 (2006)
E. López, S.V. Buldyrev, S. Havlin, H.E. Stanley, Phys. Rev. Lett 94, 248701 (2005)
W.-X. Wang, B.-H. Wang, C.-Y. Yin, Y.-B. Xie, T. Zhou, Phys. Rev. E 73, 026111 (2006)
R. Yang, W.-X. Wang, Y.-C. Lai, G. Chen, Phys. Rev. E 79, 026112 (2009)
E. Katifori, G.J. Szöllősi, M.O. Magnasco, Phys. Rev. Lett. 104, 048704 (2010)
S. Sreenivasan, R. Cohen, E. López, Z. Toroczkai, H.E. Stanley, Phys. Rev. E 75, 036105 (2007)
B. Danila, Y. Yu, J.A. Marsh, K.E. Bassler, Phys. Rev. E 74, 046106 (2006)
A.K. Chandra, P. Raghavan, W.L. Ruzzo, R. Smolensky, P. Tiwari, Comput. Complex. 6, 312 (1997)
D.J. Aldous, J. Fill, to be published in Reversible Markov Chains and Random Walks, http://www.stat.berkeley.edu/˜aldous/RWG/book.html
G. Korniss, Phys. Rev. E 75, 051121 (2007)
M.-B. Hu, W.-X. Wang, R. Jiang, Q.-S. Wu, Y.-H. Wu, Europhys. Lett. 79, 14003 (2007)
X. Ling, M.-B. Hu, W.-B. Du, R. Jiang, Y.-H. Wu, Q.-S. Wu, Phys. Lett. A 374, 4825 (2010)
B. Danila, Y. Yu, S. Earl, J.A. Marsh, Z. Toroczkai, K.E. Bassler, Phys. Rev. E 74, 046114 (2006)
A. Asztalos, Z. Toroczkai, Europhys. Lett. 92, 50008 (2010)
J.S. Andrade Jr., H.J. Herrmann, R.F.S. Andrade, L.R. da Silva, Phys. Rev. Lett. 94, 018702 (2005)
D.-S. Lee, H. Rieger, Europhys. Lett. 73, 471 (2006)
G. Korniss, M.B. Hastings, K.E. Bassler, M.J. Berryman, B. Kozma, D. Abbott, Phys. Lett. A 350, 324 (2006)
P. Prusinkiewicz, M. Allen, A. Escobar-Gutiérrez, T.M. Dejong, in Functional-Structural Plant Modelling in Crop Production, edited by J. Vos, L.F.M. Marcelis, P.H.B. de Visser, P.C. Struik, J.B. Evers (Springer, 2007), pp. 123–137
I. Fatt, Trans. AIME 207, 144 (1956)
S. Kirkpatrick, Phys. Rev. Lett. 27, 1722 (1971)
M.E.J. Newman, M. Girvan, Phys. Rev. E 69, 026113 (2004)
R. Kaul, Y. Yun, S.-G. Kim, Commun. ACM 52, 132 (2009)
P.G. Doyle, J.L. Snell, Random Walks and Electric Networks, Carus Mathematical Monograph Series (The Mathematical Association of America, Washington, DC, 1984), Vol. 22, pp. 83–149, e-print arXiv:math.PR/0001057
P. Tetali, J. Theor. Probab. 4, 101 (1991)
S. Redner, in Encyclopedia of Complexity and Systems Science, edited by R.A. Meyers (Springer New York, 2009), pp. 3737–3754
A. Ghosh, S. Boyd, A. Saberi, SIAM Rev. 50, 37 (2008)
W. Ellens et al., Linear Algebra Appl. 435, 2491 (2011)
A. Tizghadam, A. Leon-Garcia, in Proc. of IEEE Global Telecomm. Conf. (2008), pp. 1–6
A. Tizghadam, A. Leon-Garcia, IEEE Netw. 24, 10 (2010)
Z. Wu, L.A. Braunstein, V. Colizza, R. Cohen, S. Havlin, H.E. Stanley, Phys. Rev. E 74, 056104 (2006)
A. Baronchelli, R. Pastor-Satorras, Phys. Rev. E 82, 011111 (2010)
A. Barrat, M. Barthélemy, R. Pastor-Satorras, A. Vespignani, Proc. Natl. Acad. Sci. USA 101, 3747 (2004)
P.J. MacDonald, E. Almaas, A.L. Barabási, Europhys. Lett. 72, 308 (2005)
G. Korniss, R. Huang, S. Sreenivasan, B.K. Szymanski, in Handbook of Optimization in Complex Networks, edited by T. Thai, P. Pardalos, Springer Optimization and Its Applications (Springer New York, 2012), Vol. 58, pp. 61–96
V. Hernandez, J.E. Roman, V. Vidal, ACM Trans. Math. Softw. 31, 351 (2005)
M.E.J. Newman, Social Netw. 27, 39 (2005)
U. Brandes, D. Fleischer, in Lecture Notes in Computer Science, edited by V. Diekert, B. Durand (Springer, New York, 2005), Vol. 3404, pp. 533–544
K.-I. Goh, B. Kahng, D. Kim, Phys. Rev. Lett. 87, 278701 (2001)
K.-I. Goh, B. Kahng, D. Kim, Physica A 318, 72 (2003)
M. Molloy, B.A. Reed, Random Struct. Algorithms 6, 161 (1995)
M. Boguñá, R. Pastor-Satorras, A. Vespignani, Eur. Phys. J. B 38, 205 (2004)
R. Huang, Master’s thesis, Rensselaer Polytechnic Institute, Troy, New York, 2010
A.L. Barabási, R. Albert, Science 286, 509 (1999)
P. Erdős, A. Rényi, Public. Math. 6, 290 (1959)
M.E.J. Newman, Phys. Rev. E 67, 026126 (2003)
L.C. Freeman, Sociometry 40, 35 (1977)
U. Brandes, Social Netw. 30, 136 (2008)
V. Jacobson, in Proc. of ACM SIGCOMM’88 (Stanford, CA, 1988), pp. 314–329
J.D. Sachs, Sci. Amer. 300, 34 (2009)
Y. Moreno, J.B. Gómez, A.F. Pacheco, Europhys. Lett. 58, 630 (2002)
A.E. Motter, Y.-C. Lai, Phys. Rev. E 66, 065102(R) (2002)
P. Holme, B.J. Kim, C.N. Yoon, S.K. Han, Phys. Rev. E 65, 056109 (2002)
P. Crucitti, V. Latora, M. Marchiori, Phys. Rev. E 69, 045104(R) (2004)
L. de Arcangelis, S. Redner, H.J. Herrmann, J. Phys. Lett. 46, L585 (1985)
L. de Arcangelis, S. Redner, A. Coniglio, Phys. Rev. B 31, 4725 (1985)
L. de Arcangelis, A. Coniglio, S. Redner, Phys. Rev. B 36, 5631 (1987)
P.M. Duxbury, P.D. Beale, C. Moukarzel, Phys. Rev. B 51, 3476 (1995)
J.M. Smith, Annu. Rev. Ecol. Syst. 9, 31 (1978)
S.A. Kauffman, E.D. Weinberger, J. Theor. Probab. 141, 211 (1989)
A.E. Motter, C.S. Zhou, J. Kurths, Europhys. Lett. 69, 334 (2005)
R. Yang, T. Zhou, Y.-B. Xie, Y.-C. Lai, B.-H. Wang, Phys. Rev. E 78, 066109 (2008)
A.E. Motter, Phys. Rev. Lett. 93, 098701 (2004)
Y. Hayashi, T. Miyazaki, Emergent Rewirings for Cascades on Correlated Networks (2005), arXiv:cond-mat/0503615
H. Zhao, Z.Y. Gao, Eur. Phys J. B 57, 95 (2007)
M. Schäfer, J. Scholz, M. Greiner, Phys. Rev. Lett. 96, 108701 (2006)
K. Hu, T. Hu, Y. Tang, J. Stat. Phys. 141, 555 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Asztalos, A., Sreenivasan, S., Szymanski, B. et al. Distributed flow optimization and cascading effects in weighted complex networks. Eur. Phys. J. B 85, 288 (2012). https://doi.org/10.1140/epjb/e2012-30122-3
Received:
Revised:
Published:
DOI: https://doi.org/10.1140/epjb/e2012-30122-3