Random walks in weighted networks with a perfect trap: An application of Laplacian spectra

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 87, Issue 6, 2013, Pages

  Lin, Yuan ^a   Zhang, Zhongzhi ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

COMPLETE NETWORKS; CONNECTED NETWORKS; EIGENVALUES AND EIGENVECTORS; LAPLACIAN MATRICES; LAPLACIAN SPECTRA; MEAN FIRST-PASSAGE TIME; SPECTRAL GRAPH THEORY; WEIGHTED NETWORKS;

EIGENVALUES AND EIGENFUNCTIONS; GRAPH THEORY; MATRIX ALGEBRA; RANDOM PROCESSES;

DISTRIBUTED PARAMETER NETWORKS;

ALGORITHM; BIOLOGICAL MODEL; COMPUTER SIMULATION; MATHEMATICAL COMPUTING; STATISTICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; MODELS, BIOLOGICAL; MODELS, STATISTICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED;

EID: 84879891970     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.87.062140     Document Type: Article

References (95)

1. E. W. Montroll, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1664902 10, 753 (1969).
2. F. Jasch and A. Blumen, Phys. Rev. E 1063-651X 10.1103/PhysRevE.63.041108 63, 041108 (2001).
3. M. F. Shlesinger, Nature (London) NATUAS 0028-0836 10.1038/443281a 443, 281 (2006). (Pubitemid 44435133)
4. A. Bar-Haim, J. Klafter, and R. Kopelman, J. Am. Chem. Soc. JACSAT 0002-7863 10.1021/ja970972f 119, 6197 (1997). (Pubitemid 27314856)
5. A. Bar-Haim and J. Klafter, J. Phys. Chem. B JPCBFK 1520-6106 10.1021/jp980174r 102, 1662 (1998).
6. J. L. Bentz, F. N. Hosseini, and J. J. Kozak, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/S0009-2614(03)00108-8 370, 319 (2003). (Pubitemid 36280168)
7. J. L. Bentz and J. J. Kozak, J. Lumin. JLUMA8 0022-2313 10.1016/j.jlumin.2005.10.004 121, 62 (2006). (Pubitemid 43776938)
8. E. Agliari, Physica A PHYADX 0378-4371 10.1016/j.physa.2011.01.021 390, 1853 (2011).
9. I. M. Sokolov, J. Mai, and A. Blumen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.857 79, 857 (1997).
10. A. Blumen and G. Zumofen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.442086 75, 892 (1981).
11. F. Fouss, A. Pirotte, J.-M. Renders, and M. Saerens, IEEE Trans. Knowl. Data Eng. ITKEEH 1041-4347 10.1109/TKDE.2007.46 19, 355 (2007). (Pubitemid 46374533)
12. Y. Lin, A. Julaiti, and Z. Z. Zhang, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.4754735 137, 124104 (2012).
13. S. Hwang, D.-S. Lee, and B. Kahng, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.109.088701 109, 088701 (2012).
14. S. Hwang, D.-S. Lee, and B. Kahng, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.046110 85, 046110 (2012).
15. S. Hwang, D.-S. Lee, and B. Kahng, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.87.022816 87, 022816 (2013).
16. S. Redner, A Guide to First-Passage Processes (Cambridge University Press, Cambridge, 2001).
17. L. Lováz, Combinatorics, Paul Erdös Is Eighty Vol. 2, edited by, D. Miklós, V. T. Só, and, T. Szönyi, (Jáos Bolyai Mathematical Society, Budapest, 1996), pp. 353-398 [http://www.cs.elte.hu/ ~lovasz/survey.html].
18. R. Metzler and J. Klafter, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/37/31/R01 37, R161 (2004). (Pubitemid 39063557)
19. R. Burioni and D. Cassi, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/ 38/8/R01 38, R45 (2005). (Pubitemid 40306586)
20. A. Bar-Haim and J. Klafter, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.477135 109, 5187 (1998). (Pubitemid 128678689)
21. R. A. Garza-López and J. J. Kozak, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/j.cplett.2005.02.078 406, 38 (2005). (Pubitemid 40454442)
22. R. A. Garza-López, A. Linares, A. Yoo, G. Evans, and J. J. Kozak, Chem. Phys. Lett. CHPLBC 0009-2614 10.1016/j.cplett.2006.01.086 421, 287 (2006).
23. A. García Cantú and E. Abad, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.031121 77, 031121 (2008). (Pubitemid 351439070)
24. B. Kahng and S. Redner, J. Phys. A: Math. Gen. JPHAC5 0305-4470 10.1088/0305-4470/22/7/019 22, 887 (1989).
25. E. Agliari, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.011128 77, 011128 (2008). (Pubitemid 351205586)
26. C. P. Haynes and A. P. Roberts, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.78.041111 78, 041111 (2008).
27. Z. Z. Zhang, Y. Lin, S. G. Zhou, B. Wu, and J. H. Guan, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/11/10/103043 11, 103043 (2009).
28. Y. Lin, B. Wu, and Z. Z. Zhang, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.031140 82, 031140 (2010).
29. Z. Z. Zhang, B. Wu, and G. R. Chen, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/96/40009 96, 40009 (2011).
30. J. J. Kozak and V. Balakrishnan, Phys. Rev. E 1063-651X 10.1103/PhysRevE.65.021105 65, 021105 (2002). (Pubitemid 40619364)
31. J. J. Kozak and V. Balakrishnan, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 10.1142/S0218127402006138 12, 2379 (2002). (Pubitemid 36156094)
32. J. L. Bentz, J. W. Turner, and J. J. Kozak, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.011137 82, 011137 (2010).
33. B. Wu, Y. Lin, and Z. Z. Zhang, G. R. Chen J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.4737635 137, 044903 (2012).
34. Y. Lin and Z. Z. Zhang, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.4793309 138, 095905 (2013).
35. Z. Z. Zhang, Y. Qi, S. G. Zhou, S. Y. Gao, and J. H. Guan, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.81.016114 81, 016114 (2010).
36. Z. Z. Zhang, X. T. Li, Y. Lin, and G. R. Chen, J. Stat. Mech. 10.1088/1742-5468/2011/08/P08013 (2011) P08013.
37. H. X. Liu and Z. Z. Zhang, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.4794921 138, 114904 (2013).
38. A. Kittas, S. Carmi, S. Havlin, and P. Argyrakis, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/84/40008 84, 40008 (2008).
39. Z. Z. Zhang, Y. Qi, S. G. Zhou, W. L. Xie, and J. H. Guan, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.021127 79, 021127 (2009).
40. Z. Z. Zhang, J. H. Guan, W. L. Xie, Y. Qi, and S. G. Zhou, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/86/10006 86, 10006 (2009).
41. Z. Z. Zhang, W. L. Xie, S. G. Zhou, M. Li, and J. H. Guan, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.061111 80, 061111 (2009).
42. E. Agliari and R. Burioni, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.031125 80, 031125 (2009).
43. Z. Z. Zhang, Y. Lin, S. Y. Gao, S. G. Zhou, J. H. Guan, and M. Li, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.051120 80, 051120 (2009).
44. V. Tejedor, O. Bénichou, and R. Voituriez, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.065104 80, 065104 (R) (2009).
45. E. Agliari, R. Burioni, and A. Manzotti, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.011118 82, 011118 (2010).
46. Z. Z. Zhang, Y. H. Yang, and S. Y. Gao, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2011-20564-4 84, 331 (2011).
47. Z. Z. Zhang, Y. H. Yang, and Y. Lin, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.011106 85, 011106 (2012).
48. B. Meyer, E. Agliari, O. Bénichou, and R. Voituriez, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.026113 85, 026113 (2012).
49. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwanga, Phys. Rep. PRPLCM 0370-1573 10.1016/j.physrep.2005.10.009 424, 175 (2006). (Pubitemid 43135890)
50. A. Barrat, M. Barthélemy, R. Pastor-Satorras, and A. Vespignani, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0400087101 101, 3747 (2004). (Pubitemid 38381049)
51. P. J. Macdonald, E. Almaas, and A.-L. Barabási, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2005-10232-x 72, 308 (2005). (Pubitemid 41525291)
52. X. W. Chu, Z. Z. Zhang, J. H. Guan, and S. G. Zhou, Physica A PHYADX 0378-4371 10.1016/j.physa.2010.09.038 390, 471 (2011).
53. Z. M. Yang and T. Zhou, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.056106 85, 056106 (2012).
54. G. H. Zhu, G. R. Chen, X. J. Xu, and X. C. Fu, J. Theor. Biol. JTBIAP 0022-5193 10.1016/j.jtbi.2012.09.036 317, 011 (2013).
55. M. Tang, Z. H. Liu, and J. Zhou, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.74.036101 74, 036101 (2006). (Pubitemid 44330095)
56. C. Zhou, A. E. Motter, and J. Kurths, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.034101 96, 034101 (2006). (Pubitemid 43248114)
57. G. Korniss, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.75.051121 75, 051121 (2007). (Pubitemid 47140183)
58. W. X. Wang and G. R. Chen, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.026101 77, 026101 (2008). (Pubitemid 351389006)
59. B. Mirzasoleiman, M. Babaei, M. Jalili, and M. A. Safari, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.84.046114 84, 046114 (2011).
60. H.-X. Yang, W.-X. Wang, Z.-X. Wu, Y.-C. Lai, and B.-H. Wang, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.056107 79, 056107 (2009).
61. P. Buesser and M. Tomassini, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.016107 85, 016107 (2012).
62. A. Baronchelli and R. Pastor-Satorras, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.011111 82, 011111 (2010).
63. S. Kwon, W. Choi, and Y. Kim, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.82.021108 82, 021108 (2010).
64. J. J. Ramasco and B. Goncalves, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.76.066106 76, 066106 (2007).
65. Y. C. Zhang, Z. Z. Zhang, J. H. Guan, and S. G. Zhou, J. Stat. Mech.: Theory Exp. 10.1088/1742-5468/2011/10/P10001 (2011) P10001.
66. A. Baronchelli, C. Castellano, and R. Pastor-Satorras, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.066117 83, 066117 (2011).
67. Y. C. Zhang, S. Zhou, Z. Z. Zhang, J. H. Guan, S. G. Zhou, and G. R. Chen, IEEE Circ. Syst. Mag. 1531-636X 10.1109/MCAS.2011.2181075 44, 33 (2012).
68. A. C. Wu, X. J. Xu, Z. X. Wu, and Y. H. Wang, Chin. Phys. Lett. CPLEEU 0256-307X 10.1088/0256-307X/24/2/077 24, 577 (2007).
69. A. Fronczak and P. Fronczak, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.80.016107 80, 016107 (2009).
70. Z. Z. Zhang, T. Shan, and G. R. Chen, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.87.012112 87, 012112 (2013).
71. A. Barrat, M. Barthélemy, and A. Vespignani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.228701 92, 228701 (2004).
72. Z. Z. Zhang, A. Julaiti, B. Y. Hou, H. J. Zhang, and G. R. Chen, Eur. Phys. J. B EPJBFY 1434-6028 10.1140/epjb/e2011-20834-1 84, 691 (2011).
73. A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications (Springer, New York, 1974).
74. S. L. Campbell and C. D. Meyer, Generalized Inverses of Linear Transformations (Pitman, London, 1979).
75. F. Chung, Spectral Graph Theory (American Mathematical Society, Providence, RI, 1997).
76. E. M. Bollt and D. ben-Avraham, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/7/1/026 7, 26 (2005). (Pubitemid 41093488)
77. M. Popović, H. Štefančić, and V. Zlatić, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.109.208701 109, 208701 (2012).
78. A.-L. Barabási and R. Albert, Science SCIEAS 0036-8075 10.1126/science.286.5439.509 286, 509 (1999).
79. R. Pastor-Satorras, A. Vázquez, and A. Vespignani, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.258701 87, 258701 (2001).
80. Y.-Y. Liu, J.-J. Slotine, and A.-L. Barabási, Nature (London) NATUAS 0028-0836 10.1038/nature10011 473, 167 (2011).
81. A. P. Riascos and J. L. Mateos, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.86.056110 86, 056110 (2012).
82. D. Brockmann, L. Hufnagel, and T. Geisel, Nature (London) NATUAS 0028-0836 10.1038/nature04292 439, 462 (2006). (Pubitemid 43152835)
83. C. Brown, L. Liebovitch, and R. Glendon, Hum. Ecol. 0300-7839 10.1007/s10745-006-9083-4 35, 129 (2007).
84. I. Rhee, M. Shin, S. Hong, K. Lee, S. J. Kim, and S. Chong, IEEE/ACM Trans. Networking IEANEP 1063-6692 10.1109/TNET.2011.2120618 19, 630 (2011).
85. N. Scafetta, Chaos CHAOEH 1054-1500 10.1063/1.3645184 21, 043106 (2011).
86. F. Radicchi, A. Baronchelli, and L. A. N. Amaral, PLoS ONE 1932-6203 10.1371/journal.pone.0029910 7, e29910 (2012).
87. F. Radicchi and A. Baronchelli, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.85.061121 85, 061121 (2012).
88. G. M. Viswanathan, M. G. E. da Luz, E. P. Raposo, and H. E. Stanley, The Physics of Foraging (Cambridge University Press, New York, 2011).
89. D. W. Sims, E. J. Southall, N. E. Humphries, G. C. Hays, C. J. A. Bradshaw, J. W. Pitchford, A. James, M. Z. Ahmed, A. S. Brierley, M. A. Hindell, D. Morritt, M. K. Musyl, D. Righton, E. L. C. Shepard, V. J. Wearmouth, R. P. Wilson, M. J. Witt, and J. D. Metcalfe, Nature (London) NATUAS 0028-0836 10.1038/nature06518 451, 1098 (2008). (Pubitemid 351317439)
90. M. de Jager, F. J. Weissing, P. M. J. Herman, B. A. Nolet, and J. van de Koppel, Science SCIEAS 0036-8075 10.1126/science.1201187 332, 1551 (2011).
91. R. Lambiotte, R. Sinatra, J.-C. Delvenne, T. S. Evans, M. Barahona, and V. Latora, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.84.017102 84, 017102 (2011).
92. B. Zhou, Linear Algebra Appl. LAAPAW 0024-3795 10.1016/j.laa.2008.06.023 429, 2239 (2008).
93. J. Gomez-Gardeñes and V. Latora, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.78.065102 78, 065102 (R) (2008).
94. Z. Burda, J. Duda, J. M. Luck, and B. Waclaw, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.102.160602 102, 160602 (2009).
95. R. Sinatra, J. Gómez-Gardeñes, R. Lambiotte, V. Nicosia, and V. Latora, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.030103 83, 030103 (R) (2011).