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In the last few years, the complex network has received considerable attention. It is proven that the small-word effect and scale-free property exist in various real-life networks. In this paper, based on the deterministic fractal—the Sierpinski gasket, two deterministic complex network evolving models, S-DSWN and S-DSFN, are proposed by iterative approach. S-DSWN can generate small-world network, while S-DSFN can generate scale-free networks. The iterative algorithms to generate the models are also designed. Then, some relevant characteristics of the networks, such as degree distribution, clustering coefficient, and diameter, are computed or predicted analytically, which match well with the characterizations of various real-life networks. Finally, an integrated model is introduced to unify S-DSWN and S-DSFN into the same framework, which makes it convenient to study the complexity of the real networked systems within the framework of complex network theory. Moreover, we have proven that these network models are maximal planar graphs.
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Keywords:
- complex networks /
- small-world networks /
- scale-free networks /
- evolving models
[1] ［1］Strogatz S H 2001 Nature 410 268
[2] ［2］Albert R, Barabási A L 2002 Reviews of Modern Physics 74 47
[3] ［3］Dorogovtsev S N, Mendes J F F 2002 Advances in Physics 51 1079
[4] ［4］Wang X F 2002 Int. J. Bifurcat Chaos 12 885
[5] ［5］Newman M E J 2003 SIAM Review 45 167
[6] ［6］Watts D J, Strogatz S H 1998 Nature 393 440
[7] ［7］Barabási A L, Albert R 1999 Science 286 509
[8] ［8］Newman M E J, Watts D J 1999 Physics. Letters. A 263 341
[9] ［9］Newman M E J, Watts D J 1999 Physical Review E 60 7332
[10] ］Liu jianguo, Dang yanzhong, Wang zhongtuo 2006 Chinese Physics Letters 23 46
[11] ］Li X, Chen G R 2003 Physica A 328 274
[12] ］Barabási A L, Ravasz E, Vicsek T 2001 Physica A 299 559
[13] ］Comellas F, Ozón J, Peters J G 2000 Inf. Process. Lett. 76 83
[14] ］Dorogovtsev S N, Goltsev A V, Mendes J F F 2002 Physical Review E 65 066122.
[15] ］Andrade J S, Herrmann HJ, Andrade R F S. 2005 Physical Review Letters 94 018702
[16] ］Zhang Z Z, Comellas F, Fertin G 2006 J.Phys.A: Math.Gen. 39 1811
[17] ］Zhang Z Z, Lili Ronga, Francesc Comellas 2006 Physica A 364 618
[18] ］Zhang Z Z, Rong L L, Zhou S G 2006 Physical Review E 74 046105.
[19] ］Zhang Z Z, Zhou S G 2007 Eur. Phys. J. B 60 259
[20] ］Zhang Z Z, Rong L L, Guo C H 2006 Physica A 363 567
[21] ］Jost J, Joy M P 2002 Physical Review E 66 036126.
[22] ］Haynes C P, Roberts A P 2008 Phys. Rev. E 78 041111
[23] ］Majewski M 1998 Comput. & Graphics 22 129
[24] ］Zhang Z Z 2007 EPL79 38007
[25] ］Ravasz E, Barabási A L 2003 Physical Review E 67 026112
[26] ］Zhou T, Yan G, Wang BH 2005 Phys. Rev. E 71 046141
[27] ］Hambly B M 1997 Annals of probability 25 1059
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[1] ［1］Strogatz S H 2001 Nature 410 268
[2] ［2］Albert R, Barabási A L 2002 Reviews of Modern Physics 74 47
[3] ［3］Dorogovtsev S N, Mendes J F F 2002 Advances in Physics 51 1079
[4] ［4］Wang X F 2002 Int. J. Bifurcat Chaos 12 885
[5] ［5］Newman M E J 2003 SIAM Review 45 167
[6] ［6］Watts D J, Strogatz S H 1998 Nature 393 440
[7] ［7］Barabási A L, Albert R 1999 Science 286 509
[8] ［8］Newman M E J, Watts D J 1999 Physics. Letters. A 263 341
[9] ［9］Newman M E J, Watts D J 1999 Physical Review E 60 7332
[10] ］Liu jianguo, Dang yanzhong, Wang zhongtuo 2006 Chinese Physics Letters 23 46
[11] ］Li X, Chen G R 2003 Physica A 328 274
[12] ］Barabási A L, Ravasz E, Vicsek T 2001 Physica A 299 559
[13] ］Comellas F, Ozón J, Peters J G 2000 Inf. Process. Lett. 76 83
[14] ］Dorogovtsev S N, Goltsev A V, Mendes J F F 2002 Physical Review E 65 066122.
[15] ］Andrade J S, Herrmann HJ, Andrade R F S. 2005 Physical Review Letters 94 018702
[16] ］Zhang Z Z, Comellas F, Fertin G 2006 J.Phys.A: Math.Gen. 39 1811
[17] ］Zhang Z Z, Lili Ronga, Francesc Comellas 2006 Physica A 364 618
[18] ］Zhang Z Z, Rong L L, Zhou S G 2006 Physical Review E 74 046105.
[19] ］Zhang Z Z, Zhou S G 2007 Eur. Phys. J. B 60 259
[20] ］Zhang Z Z, Rong L L, Guo C H 2006 Physica A 363 567
[21] ］Jost J, Joy M P 2002 Physical Review E 66 036126.
[22] ］Haynes C P, Roberts A P 2008 Phys. Rev. E 78 041111
[23] ］Majewski M 1998 Comput. & Graphics 22 129
[24] ］Zhang Z Z 2007 EPL79 38007
[25] ］Ravasz E, Barabási A L 2003 Physical Review E 67 026112
[26] ］Zhou T, Yan G, Wang BH 2005 Phys. Rev. E 71 046141
[27] ］Hambly B M 1997 Annals of probability 25 1059
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