Matrix representation of evolving networks

Acta Physica Polonica B

Volumn 36, Issue 8, 2005, Pages 2523-2536

  Malarz, Krzysztof ^a   KuŁakowski, Krzysztof ^a  

^a AGH UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

DATA REDUCTION; NUMERICAL METHODS; STATISTICAL METHODS; TOPOLOGY;

EVOLVING NETWORKS; MATRIX REPRESENTATION; NUMERICAL DATA;

RANDOM PROCESSES;

EID: 27744452869     PISSN: 05874254     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (81)

1. J. Clark, D.A. Holton, A First Look at Graph Theory, World Scientific, 1991;
2. R.J. Wilson, Introduction to Graph Theory, Addison-Wesley, 1996.
3. R. Albert, A.-L. Barabási, Rev. Mod. Phys. 286, 47 (2002).
4. S.N. Dorogovtsev, J.F.F. Mendes, Adv. Phys. 51, 1079 (2002).
5. M.E.J. Newman, SIAM Rev. 45, 167 (2003).
6. S.N. Dorogovtsev, J.F.F. Mendes, A.N. Samukhin, Nucl. Phys. B653, 307 (2003).
7. F. Liljeros, C.R. Edling, L.A.N. Amaral, H.E. Stanley, Y. Aberg, Nature 411, 907 (2001);
8. M. Lässig, U. Bastolla, S.C. Manrubia, A. Valleriani, Phys. Rev. Lett. 86, 4418 (2001);
9. J. Camacho, R. Guimerà, L.A.N. Amaral, Phys. Rev. E65, 030901 (R) (2002);
10. J. Camacho, R. Guimerà, L.A.N. Amaral, Phys. Rev. Lett. 88, 228102 (2002).
11. S. Render, Eur. Phys. J. B4, 131 (1998);
12. A. Vázquez, cond-mat/0105031.
13. M.E.J. Newmann, Phys. Rev. E64, 016131 (2001);
14. M.E.J. Newmann, Phys. Rev. E64, 016132 (2001);
15. M.V. Simkin, V.P. Roychowdhury, Complex Syst. 14, 269 (2003);
16. M.V. Simkin, V.P. Roychowdhury, Annals Improb. Res. 11, 24 (2005);
17. T. Erez, S. Moldovan, S. Solomon, cond-mat/0406695;
18. S. Galam, A. Mauger, Physica A 323, 695 (2003);
19. S. Galam, Physica A 336, 49 (2004);
20. S. Galam, Eur. Phys. J. B26, 269 (2002);
21. D. Stauffer, cond-mat/0204099;
22. S. Galam, Eur. Phys. J. B26, 269 (2002);
23. A. Proykova, D. Stauffer, Physica A 312, 300 (2002);
24. S. Solomon, G. Weisbuch, L. de Arcangelis, N. Jan, D. Stauffer, Physica A 277, 239 (2000).
25. R.N. Mantegna, H.E. Stanley, Introduction to Econophysics Cambridge University Press, 2000;
26. A. Barrañón, nlin.AO/0404009;
27. M. Hohnisch, S. Pittnauer, D. Stauffer, cond-mat/0308358;
28. D. Makowiec, P. Gnaciński, W. Miklaszeski, cond-mat/0307290;
29. J. Goldenberg, B. Libai, S. Solomon, N. Jan, D. Stauffer, Physica A 284, 335 (2000).
30. B. Shargel, H. Sayama, I. R. Epstein, Y. Bar-Yam, Phys. Rev. Lett. 90, 068701 (2003);
31. D. Magoni, IEEE J. Selected Areas Commun. 21, 949 (2003);
32. P. Crucitti, V. Latora, M. Marchiori, A. Rapisarda, Physica A 320, 622 (2003);
33. B. Shargel, H. Sayama, I. R. Epstein, Y. Bar-Yam, Phys. Rev. Lett. 90, 068701 (2003);
34. A.E. Motter, T. Nishikawa, L. Ying-Cheng, Phys. Rev. E66, 65103 (2002);
35. G.-J. Lin, X. Cheng, Q. Ou-Yang, Chinese Phys. Lett. 20, 22 (2003);
36. L. Zonghua, L. Ying-Cheng, Y. Nong, Phys. Rev. E66, 36112 (2002);
37. L. Zonghua, L. Ying-Cheng, Y. Nong, P. Dasgupta, Phys. Lett. A303, 337 (2002);
38. S.N. Dorogovtsev, J.F.F. Mendes, R. Cohen, K. Erez, D. benAvraham, S. Havlin, Phys. Rev. Lett. 87, 219801 (2001);
39. R. Cohen, K. Erez, D. Ben-Avraham, S. Havlin, Phys. Rev. Lett. 86, 3682 (2001);
40. A.-L. Barabási, R. Albert, H. Jeong, Physica A 281, 69 (2000);
41. K.M. King, Educom. Bulletin 23, 5 (1988);
42. W.H. Cunningham, J. Assoc. Comput. Machinery 32, 549 (1985).
43. R. Albert, A.-L. Barabási, Science 286, 509 (1999).
44. D.J. Watts, S.H. Strogatz, Nature 393, 440 (1998).
45. P. Erdos, A. Rényi, Publications Mathematicae 6, 290 (1959);
46. P. Erdos, A. Rényi, Publ. Math. Inst. Hung. Acad. Sci. 5, 17 (1960).
47. S.N. Dorogovtsev, J.F.F. Mondes, cond-mat/0404593.
48. Z. Burda, J.D. Correia, A. Krzywicki, Phys. Rev. E64, 046118 (2001).
49. W. de Nooy, A. Mrvar, V. Batagelj, Exploratory Social Network Analysis with Pajek, Cambridge UP, 2005;
50. P. Doreian, V. Batagelj, A. Ferligoj, Generalized Blockmodeling, Cambridge UP, 2005; http://vlado.fmf.uni-lj.si/pub/networks/pajek/.
51. H.P. Schultz, J. Chem. Inf. Comput. Sci. 40, 1158 (2000);
52. W.R. Müller, K. Szymanski, J.V. Knop, N. Trinajstić, J. Compt. Chem. 8, 170 (1987).
53. T.H. Cormen, C.E. Leiserson, R.L. Rivest, Introduction to Algorithms, MIT Press, 2001.
54. K. Malarz, J. Czaplicki, B. Kawecka-Magiera, K. Kułakowski, Int. J. Mod. Phys. C14, 1201 (2003).
55. K. Malarz, J. Karpińska, A. Kardas, K. Kułakowski, TASK Quarterly 8, 115 (2004).
56. K. Malarz, K. Kułakowski, Eur. Phys. J. B41, 333 (2004).
57. K. Malarz, K. Kułakowski, Physica A 345, 326 (2005).
58. D. Stauffer, private communnication.
59. Z. Burda, J. Erdmann, B. Petersson, M. Wattenberg, Phys. Rev. E67, 026105 (2003).
60. A.-L. Barabási, Phys. World, July 2001.
61. S. Milgram, Psychol. Today 2, 60 (1967);
62. J. Travers, S. Milgram, Sociometry 32, 425 (1969);
63. http://smallworld.columbia.edu/.
64. B.J. Kim, C.N. Yoo, S.K. Han, H. Jeong, Phys. Rev. E65, 027103 (2002);
65. L.A. Adamic, R.M. Lukose, A.R. Puniyani, B.A. Huberman, Phys. Rev. E64, 046135 (2001).
66. M.R. Garey, D.S. Johnson, Computers and Intractability. A Guide to the Theory of NP-Completeness, Freeman, New York 1979.
67. K. Malarz, J. Karpińska, K. Kułakowski, B. Tadić, cond-mat/0503760;
68. B. Tadić, K. Malarz , K. Kułakowski, Phys. Rev. Lett. 94, 137204 (2005);
69. D. Stauffer, K. Kułakowski, TASK Quarterly 7, 257 (2003);
70. J. Bonnekoh, Int. J. Mod. Phys. C14, 1231 (2003);
71. K. Malarz, Int. J. Mod. Phys. C14, 561 (2003);
72. A.S. Elgazzar, Physica A 324, 402 (2003);
73. P.R.A. Campos, V.M. de Oliveira, F.G.B. Moreira, Phys. Rev. E67, 26104 (2003);
74. S.N. Dorogovtsev, A.V. Goltsev, J.F.F. Mendes, Phys. Rev. E66, 016104 (2002);
75. A. Aleksiejuk, J.A. Hołyst, D. Stauffer, Physica A 310, 260 (2002);
76. M. Kuperman, D. Zanette, Eur. Phys. J. B26, 387 (2002);
77. H. Hong, B.J. Kim, M.Y. Choi, Phys. Rev. E66, 018101 (2002);
78. P. Svenson, D.A. Johnston, Phys. Rev. E65, 036105 (2002);
79. C.P. Herrero, Phys. Rev. E65, 066110 (2002);
80. A.S. Elgazzar, Int. J. Mod. Phys. C12, 1537 (2001);
81. A. Pȩkalski, Phys. Rev. E64, 057104 (2001).