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According to the existence of motif in complex network topology structure, the motif-based node degree and edge degree are proposed to measure the importance of node and edge in the network on the basis of the traditional node degree and edge clustering coefficient. The Rand-ESU algorithm is used for motif detection of eight different scale networks, and the result demonstrates the existence of motif. The Rand-ESU algorithm is also used for analyzing the motif structures and characteristics in Karate network and Dolphin network. The Pearson correlation coefficient is used to measure the correlations of motif-based node degree and traditional node degree, motif-based edge degree and edge clustering coefficient. The results of simulation analysis show that the correlations are related to the motif species. The definitions of motif-based node degree and edge degree are the improvement and development of original definitions, and they comprehensively depict the importance of node and edge in the network.
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Keywords:
- motif /
- node degree /
- edge degree /
- Pearson correlation coefficient
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[18] Zachary W W 1977 J. Anthropol. Res. 33 452
[19] Lusseau D, Schneider K, Boisseau O J 2003 Behav. Ecol. Sociobiol. 54 396
[20] Gunes I, Bingol H 2006 arXiv: cs/0610129 [cs.MA]
[21] Girvan M, Newman M E J 2002 Proc. Natl. Aead. Sci. USA 99 7821
[22] Gleiser P, Danon L 2003 Adv. Complex Syst. 6 565
[23] Ebel H, Mielsch L I, Bornholdt S 2002 Phys. Rev. E 66 035103(R)
[24] Newman M E J 2001 Phys. Rev. E 64 016131
[25] Boguna M, Pastor-Satorras R, Diaz-Guilera A, Arenas A 2004 Phys. Rev. E 70 056122
[26] Wernicke S, Rasche F 2006 Bioinformatics 22 1152
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[1] Wang X F, Li X, Chen G R 2006 Throry and Application of Complex Networks (Beijing: Tsinghua University Press) p18 (in Chinese) [汪小帆, 李翔, 陈关荣 2006 复杂网络理论及其应用(北京: 清华大学出版社)第18页]
[2] Antiqueira L, Luciano D, Costa F 2009 New J. Phys. 11 013058
[3] Shen-Orr S, Milo R, Mangan S, Alon U 2002 Nat. Genet. 31 64
[4] Milo R, Shen-Orr S, Itzkovitz S, Kashtan N, Chklovskii D, Alon U 2002 Science 298 824
[5] Barabasi A L, Oltvai Z N 2004 Nature 5 101
[6] Milo R, Itzkovitz S, Kashtan N, Levitt R, Shen-Orr S, Ayzenshtat I, Sheffer M, Alon U 2004 Science 303 1538
[7] Onnela J P, Saram_ki J, Kert_sz J, Kaski K 2005 Phys. Rev. E 71 065103(R)
[8] Luciano D, Francisco A R, Travieso G, Villas P R B 2007 Adv. Phys. 56 167
[9] Krumov L 2010 Local Structures Determine Performance within Complex Network (Darmstadt: Suedwestdeutscher Verlag fuer Hochschulschriften) p54
[10] Kotorowicz M, Kozitsky Y 2011 Condens. Matter Phys. 14 13801
[11] Squartini T, Garlaschelli D 2012 Lect. Notes. Comput. Sci. 7166 24
[12] Dong Z, Li X 2010 Acta Phys. Sin. 59 1600 (in Chinese) [董昭, 李翔 2010 物理学报 59 1600]
[13] Miao L L, Han C F, Liu L, Cao J M 2012 Stud. Sci. Sci. 30 1468 (in Chinese) [缪莉莉, 韩传峰, 刘亮, 曹吉鸣 2012 科学学研究 30 1468]
[14] Liu L, Xu W S, Han C F 2013 J. Tongji Univ. (Nat. Sci) 41 53 (in Chinese) [刘亮, 许维胜, 韩传峰 2013 同济大学学报 (自然科学版) 41 53]
[15] Zhang L, Qian G Q, Zhang L 2010 Syst. Eng-Theory Pract. 30 361 (in Chinese) [张林, 钱冠群, 张莉 2010系统工程理论与实践 30 361]
[16] Shi D H 2010 Complex Syst. Complexity Sci. 7 16 (in Chinese) [史定华 2010复杂系统与复杂性科学 7 16]
[17] Hu J, Yang B R 2009 Appl. Res. Comput. 26 858 (in Chinese) [胡健, 杨炳儒 2009计算机应用研究 26 858]
[18] Zachary W W 1977 J. Anthropol. Res. 33 452
[19] Lusseau D, Schneider K, Boisseau O J 2003 Behav. Ecol. Sociobiol. 54 396
[20] Gunes I, Bingol H 2006 arXiv: cs/0610129 [cs.MA]
[21] Girvan M, Newman M E J 2002 Proc. Natl. Aead. Sci. USA 99 7821
[22] Gleiser P, Danon L 2003 Adv. Complex Syst. 6 565
[23] Ebel H, Mielsch L I, Bornholdt S 2002 Phys. Rev. E 66 035103(R)
[24] Newman M E J 2001 Phys. Rev. E 64 016131
[25] Boguna M, Pastor-Satorras R, Diaz-Guilera A, Arenas A 2004 Phys. Rev. E 70 056122
[26] Wernicke S, Rasche F 2006 Bioinformatics 22 1152
[27] Egghe L, Leydesdorff L 2009 J. Am. Soc. Inf. Sci. Tech. 60 1027
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