Original Articles |
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Walks on Weighted Networks |
WU An-Cai1;XU Xin-Jian2;WU Zhi-Xi1;WANG Ying-Hai1 |
1Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000
2Departamento de Fisica da Universidade de Aveiro, 3810-193 Aveiro, Portugal |
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Cite this article: |
WU An-Cai, XU Xin-Jian, WU Zhi-Xi et al 2007 Chin. Phys. Lett. 24 577-580 |
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Abstract We investigate the dynamics of random walks on weighted networks. Assuming that the edge weight and the node strength are used as local information by a random walker. Two kinds of walks, weight-dependent walk and strength-dependent walk, are studied. Exact expressions for stationary distribution and average return time are derived and confirmed by computer simulations. The distribution of average return time and the mean-square displacement are calculated for two walks on the Barrat--Barthelemy--Vespignani (BBV) networks. It is found that a weight-dependent walker can arrive at a new territory more easily than a strength-dependent one.
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Keywords:
89.75.Hc
05.40.Fb
89.75.Fb
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Received: 20 July 2006
Published: 24 February 2007
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PACS: |
89.75.Hc
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(Networks and genealogical trees)
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05.40.Fb
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(Random walks and Levy flights)
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89.75.Fb
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(Structures and organization in complex systems)
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[1] Spitzer F 1976 Principles of Random Walk 2nd edn (NewYork: Springer) [2] Barber M N and Ninham B W 1970 Random and RestrictedWalks (New York: Gordon and Breach) [3] Hughes B D 1996 Random Walks and Random Environments(Oxford: Clarendon) vols 1 and 2 Erdos P and Renyi A 1959 Publ. Math. 6290 Erdos P and Renyi A 1960 Publ. Math. Inst. Hung.Acad. Sci. 5 17 [5] Watts D J and Strogatz S H 1998 Nature 393 440 [6] Barabasi A L and Albert R 1999 Science 286 509 [7] Watts D J 1999 Small Worlds: The Dynamics of NetworksBetween Order and Randomness (Princeton, NJ: Princeton University Press) [8] Dorogovtsev S N and Mendes J F F 2002 Adv. Phys. 511079 [9] Newman M E J 2003 SIAM Rev. 45 167 [10] Strogatz S H 2001 Nature 410 268 [11] Pandit S A and Amritkar R E 2001 Phys. Rev. E 63041104 [12] Lahtinen J, Kertesz J and Kaski K 2001 Phys. Rev. E 64 057105 [13] Almaas E, Kulkarni R V and Stroud D 2003 Phys. Rev. E 68 056105 [14] Parris P E and Kenkre V M 2005 Phys. Rev. E 72056119 [15] Adamic L A, Lukose R M, Puniyani A R and Huberman B A 2001 Phys. Rev. E 64 046135 [16] Noh J D and Rieger H 2004 Phys. Rev. Lett. 92 118701 Noh J D and Rieger H 2004 Phys. Rev. E 69 036111(cond-mat/0509564) [17] Gallos L K 2004 Phys. Rev. E 70 046116 [18] Yang S J 2005 Phys. Rev. E 71 016107 [19] Barrat A, Barthelemy M, Pastor-Satorras R and VespignaiA 2004 Proc. Natl. Acad. Sci. USA 101 3747 Barrat A, Barthelemy M and Vespignani A 2004 Phys. Rev. Lett. 92 228701 Barrat A, Barthelemy M and Vespignani A 2004 Phys. Rev.E 70 066149 Barrat A and Pastor-Satorras R 2005 Phys. Rev. E 71 036127 [20] Xu X J, Wu Z X and Wang Y H 2005 Chin. Phys. Lett. 22 1548 [21] Wu Z X, Xu X J and Wang Y H 2005 Phys. Rev. E 71 066124 [22] Yan G, Zhou T, Wang J, Fu Z and Wang B 2005 Chin. Phys. Lett. 22 510 [23] Simonsen I 2005 Physica A 357 317 |
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