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针对复杂网络拓扑结构中模体的存在性, 在传统的顶点度和边聚类系数定义的基础上, 提出了基于模体的顶点度和边度来衡量网络中顶点和边的重要性. 用Rand-ESU算法对不同规模的8个网络进行模体检测, 验证了网络中模体的存在性, 重点分析了Karate网络和Dolphin网络中模体的结构和特征. 用Pearson相关系数衡量基于模体的顶点度与传统顶点度、基于模体的边度与边聚类系数的相关性, 仿真分析结果表明相关性大小与模体种类有关, 基于模体的顶点度和边度是对原定义的一种改进和拓展, 更全面地刻画了顶点和边在网络中的重要性.
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关键词:
- 模体 /
- 顶点度 /
- 边度 /
- Pearson相关系数
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.-
Keywords:
- motif /
- node degree /
- edge degree /
- Pearson correlation coefficient
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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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