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In this paper, we present a new approach to partitioning communities in a complex network via degree of dependence of nodes. We define the dependence degree of a node on its neighbors, the dependencetce degree and the conditional dependence degree of a node on a cluster. The main point of the approach is to partition the nodes, which have the biggest dependence degree and are only dependent on nodes, firstly to clusters, then to absorb nodes whose dependence degree or conditional dependence degree on cluster gets the right value, until all the nodes are partitioned to the right communities. The partition of our approach in some real-world network satisfies the definition of communities, and in the network whose communities are already known, our partition method fits the physical truth.
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Keywords:
- complex network /
- community structure /
- partitioning /
- dependence degree
[1] Erds P, Rnyi A 1960 Publ. Math. Inst. Hung. Acad. Sci. 5 17
[2] Garey M R, Johnson D S 1979 Computers and Intractability: A Guide to the Theory of NP-Completeness (vol. 1) (San Francisco: Freeman Publishers) p1
[3] [4] Scott J 2002 Social Network Analysis: A Handbook (vol. 2) (London: Sage Publications) p1
[5] [6] Wang Z, Zhang J Z 2007 PLoS Computational Biology 3 e107
[7] [8] [9] Givan M, Newman M E J 2002 Proc. Natl. Acad. Sci. USA 99 7821
[10] [11] Ino H, Kudo M, Nakamura A 2005 Partitioning of web graphs by community topology Chiba, May 10-14, 2005 661
[12] [13] Zhang Z Z, Lin Y, Gao S Y, Zhou S G, Guan J H, Li M 2009 Phys. Rev. E 80 051120
[14] [15] Zhang Z Z, Yang Y H, Lin Y 2012 Phys. Rev. E 85 011106
[16] Kernighan B W, Lin S 1970 Bell System Technical Journal 49 291
[17] [18] [19] Fiedler M 1973 Czechoslovak Mathematical Journal 23 298
[20] [21] Pothen A, Simon H D, Liou K P 1990 SIAM J. Matrix Anal. Appl. 11 430
[22] Newman M E J 2004 Phys. Rev. E 69 066133
[23] [24] [25] Clauset A, Newman M E J, Moore C 2004 Phys. Rev. E 70 066111
[26] [27] Newman M E J, Girvan M 2004 Phys. Rev. E 69 026113
[28] Radicchi F, Castellano C, Cecconi F, Loreto V, Parisi D 2004 Proc. Natl. Acad. Sci. USA 101 2658
[29] [30] [31] Reichardt J, Bornholdt S 2004 Phys. Rev. Lett. 93 218701
[32] [33] Reichardt J, Bornholdt S 2006 Phys. Rev. E 93 016110
[34] Wu F, Huberman B A 2004 Eur. Phys. J. B 38 331
[35] [36] Zanjani A A H, Darooneh A H 2011 Phys. Rev. E 84 036109
[37] [38] Chen D B, Fu Y, Shang M S 2009 Phys. A 388 2741
[39] [40] [41] Pan Y, Li D H, Liu J G, Liang J Z 2010 Phys. A 389 2849
[42] Wang X Y, Li J Q 2013 Phys. A 392 2555
[43] [44] [45] Shen Y, Xu H L 2010 Acta Phys. Sin. 59 6022 (in Chinese)[沈毅, 徐焕良 2010 59 6022]
[46] Newman M E J 2004 Eur. Phys. J. B 38 321
[47] [48] [49] Yuan C, Chai Y 2012 Acta Phys. Sin. 61 218901 (in Chinese)[袁超, 柴毅 2012 61 218901]
[50] [51] Zhan W H, Zhang Z Z, Guan J H, Zhou S G 2011 Phys. Rev. E 83 066120
[52] Shen Y 2011 Chin. Phys. B 20 040511
[53] [54] Shen Y 2013 Chin. Phys. B 22 058903
[55] [56] [57] Zachary W W 1977 J. Anthropol. Res. 33 452
[58] [59] Lusseau D 2003 Proc R Soc. Lond. B 270 186
[60] [61] Tyler J, Wilkinson D, Huberman B 2005 The Information Society: An International Journal 21 81
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[1] Erds P, Rnyi A 1960 Publ. Math. Inst. Hung. Acad. Sci. 5 17
[2] Garey M R, Johnson D S 1979 Computers and Intractability: A Guide to the Theory of NP-Completeness (vol. 1) (San Francisco: Freeman Publishers) p1
[3] [4] Scott J 2002 Social Network Analysis: A Handbook (vol. 2) (London: Sage Publications) p1
[5] [6] Wang Z, Zhang J Z 2007 PLoS Computational Biology 3 e107
[7] [8] [9] Givan M, Newman M E J 2002 Proc. Natl. Acad. Sci. USA 99 7821
[10] [11] Ino H, Kudo M, Nakamura A 2005 Partitioning of web graphs by community topology Chiba, May 10-14, 2005 661
[12] [13] Zhang Z Z, Lin Y, Gao S Y, Zhou S G, Guan J H, Li M 2009 Phys. Rev. E 80 051120
[14] [15] Zhang Z Z, Yang Y H, Lin Y 2012 Phys. Rev. E 85 011106
[16] Kernighan B W, Lin S 1970 Bell System Technical Journal 49 291
[17] [18] [19] Fiedler M 1973 Czechoslovak Mathematical Journal 23 298
[20] [21] Pothen A, Simon H D, Liou K P 1990 SIAM J. Matrix Anal. Appl. 11 430
[22] Newman M E J 2004 Phys. Rev. E 69 066133
[23] [24] [25] Clauset A, Newman M E J, Moore C 2004 Phys. Rev. E 70 066111
[26] [27] Newman M E J, Girvan M 2004 Phys. Rev. E 69 026113
[28] Radicchi F, Castellano C, Cecconi F, Loreto V, Parisi D 2004 Proc. Natl. Acad. Sci. USA 101 2658
[29] [30] [31] Reichardt J, Bornholdt S 2004 Phys. Rev. Lett. 93 218701
[32] [33] Reichardt J, Bornholdt S 2006 Phys. Rev. E 93 016110
[34] Wu F, Huberman B A 2004 Eur. Phys. J. B 38 331
[35] [36] Zanjani A A H, Darooneh A H 2011 Phys. Rev. E 84 036109
[37] [38] Chen D B, Fu Y, Shang M S 2009 Phys. A 388 2741
[39] [40] [41] Pan Y, Li D H, Liu J G, Liang J Z 2010 Phys. A 389 2849
[42] Wang X Y, Li J Q 2013 Phys. A 392 2555
[43] [44] [45] Shen Y, Xu H L 2010 Acta Phys. Sin. 59 6022 (in Chinese)[沈毅, 徐焕良 2010 59 6022]
[46] Newman M E J 2004 Eur. Phys. J. B 38 321
[47] [48] [49] Yuan C, Chai Y 2012 Acta Phys. Sin. 61 218901 (in Chinese)[袁超, 柴毅 2012 61 218901]
[50] [51] Zhan W H, Zhang Z Z, Guan J H, Zhou S G 2011 Phys. Rev. E 83 066120
[52] Shen Y 2011 Chin. Phys. B 20 040511
[53] [54] Shen Y 2013 Chin. Phys. B 22 058903
[55] [56] [57] Zachary W W 1977 J. Anthropol. Res. 33 452
[58] [59] Lusseau D 2003 Proc R Soc. Lond. B 270 186
[60] [61] Tyler J, Wilkinson D, Huberman B 2005 The Information Society: An International Journal 21 81
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