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Using the theory of gravitational field, we study the gravitational field induced by the node in the process of the network transmission, establish the gravitational filed equation, and define two parameters α and γ for adjusting the dependencs of transmission data on the unblocked degree of node, the transmission capacity of node and the path length. Based on the gravitational field of node, an efficient routing strategy is proposed, and the package will be transferred along the route with maximum gravitation. In order to characterize the efficiency of the method, we introduce an order parameter η to measure the throughput of the network by the critical value of phase transition from free state to jammed state, and use the node betweenness centrality B to test the transmission efficiency of network and the congestion distribution. We simulate the network transmission efficiencies under different values of α and γ. Simulation results show that compared with the traditional shortest routing strategy, our routing strategy improves the network capacity several times, and effectively balances the distribution of the betweenness centrality of nodes, and the average path length Lavg> shows a trend from ascent to descent with the increase of load amount R, and the change of the parameters α and γ nearly have no effect on the network transmission capacity, which suggests the efficiency of our routing strategy is independent of α and γ, the network capacities are approximately equal for any values of α and γ in the feasible region.
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Keywords:
- complex network /
- gravitation field /
- routing strategy /
- congestion
[1] Newman M E J 2003 SIAM Review 45 167
[2] Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Physics Reports 424 175
[3] Mitchell M 2006 Artificial Intelligence 170 1194
[4] Newman M E J 2010 Networks: An Introduction (Volume 1) (Oxford: Oxford University Press) p11-20
[5] Wu J, Barahona M, Tan Y J, Deng H Z 2010 Chine. Phys. Lett. 27 078902
[6] Shao Z G 2010 Appl. Phys. Lett. 96 073703
[7] Toda A A 2011 Phys. Rev. E 83 046122
[8] Zager L, Verghese G 2008 Complexity 14 12
[9] Töenjes R, Masuda N, Kori H 2010 Chaos 20 033108
[10] Leyva I, Navas A, Nadal I S, Buldú J M, Almendral J A, Boccaletti S 2011 Phys. Rev. E 84 065101
[11] Daniele D M, Luca D A, Ginestra B, Matteo M 2009 Phys. Rev. E 79 015101
[12] Noh J D, Rieger H 2004 Phys. Rev. Lett. 92 118701
[13] Ramascc J J, Lama M S L, Eduardo L, Boettcher S 2010 Phys. Rev. E 82 036119
[14] Guimerá R, Díaz-Guilera A, Vega-Redondo F, Cabrales A, Arenas A 2002 Phys. Rev. Lett. 89 248701
[15] Danila B, Yu Y, Marsh J A, Bassler K E 2007 Chaos 17 026102
[16] Kawamoto H, Igarashi A 2012 Physica A 391 895
[17] Qian J H, Han D D 2009 Acta Phys. Sin. 58 3028 (in Chinese) [钱江海, 韩定定 2009 物流学报 58 3028]
[18] Liu G, Li Y S 2012 Acta Phys. Sin. 61 108901 (in Chinese) [刘刚, 李永树 2012 61 108901]
[19] Arenas A, Díaz-Guilera A, Guimerá R 2001 Phys. Rev. Lett. 86 3196
[20] Crucitti P, Latora V, Porta S 2006 Chaos 16 015113
[21] Freeman L G 1977 Sociometry 40 35
[22] Li Q Q, Zeng Z, Yang B S, Li B J 2010 Geomatics and Information Science of Wuhan University 35 37 (in Chinese) [李清泉, 曾喆, 杨必胜, 李必军 2010 武汉大学学报(信息科学版) 35 37]
[23] Barabási A L, Albert R 1999 Science 286 509
[24] Echenique P, Gomez-Gardenes J, Moreno Y 2004 Phys. Rev. E 70 056105
[25] Danila B, Sun Y D, Bassler E K 2009 Phys. Rev. E 80 066116
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[1] Newman M E J 2003 SIAM Review 45 167
[2] Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang D U 2006 Physics Reports 424 175
[3] Mitchell M 2006 Artificial Intelligence 170 1194
[4] Newman M E J 2010 Networks: An Introduction (Volume 1) (Oxford: Oxford University Press) p11-20
[5] Wu J, Barahona M, Tan Y J, Deng H Z 2010 Chine. Phys. Lett. 27 078902
[6] Shao Z G 2010 Appl. Phys. Lett. 96 073703
[7] Toda A A 2011 Phys. Rev. E 83 046122
[8] Zager L, Verghese G 2008 Complexity 14 12
[9] Töenjes R, Masuda N, Kori H 2010 Chaos 20 033108
[10] Leyva I, Navas A, Nadal I S, Buldú J M, Almendral J A, Boccaletti S 2011 Phys. Rev. E 84 065101
[11] Daniele D M, Luca D A, Ginestra B, Matteo M 2009 Phys. Rev. E 79 015101
[12] Noh J D, Rieger H 2004 Phys. Rev. Lett. 92 118701
[13] Ramascc J J, Lama M S L, Eduardo L, Boettcher S 2010 Phys. Rev. E 82 036119
[14] Guimerá R, Díaz-Guilera A, Vega-Redondo F, Cabrales A, Arenas A 2002 Phys. Rev. Lett. 89 248701
[15] Danila B, Yu Y, Marsh J A, Bassler K E 2007 Chaos 17 026102
[16] Kawamoto H, Igarashi A 2012 Physica A 391 895
[17] Qian J H, Han D D 2009 Acta Phys. Sin. 58 3028 (in Chinese) [钱江海, 韩定定 2009 物流学报 58 3028]
[18] Liu G, Li Y S 2012 Acta Phys. Sin. 61 108901 (in Chinese) [刘刚, 李永树 2012 61 108901]
[19] Arenas A, Díaz-Guilera A, Guimerá R 2001 Phys. Rev. Lett. 86 3196
[20] Crucitti P, Latora V, Porta S 2006 Chaos 16 015113
[21] Freeman L G 1977 Sociometry 40 35
[22] Li Q Q, Zeng Z, Yang B S, Li B J 2010 Geomatics and Information Science of Wuhan University 35 37 (in Chinese) [李清泉, 曾喆, 杨必胜, 李必军 2010 武汉大学学报(信息科学版) 35 37]
[23] Barabási A L, Albert R 1999 Science 286 509
[24] Echenique P, Gomez-Gardenes J, Moreno Y 2004 Phys. Rev. E 70 056105
[25] Danila B, Sun Y D, Bassler E K 2009 Phys. Rev. E 80 066116
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