메뉴 건너뛰기




Volumn 3, Issue 3, 2014, Pages 319-346

Critical phase in complex networks: A numerical study

Author keywords

Complex networks percolation; Monte carlo simulation; Phase transition

Indexed keywords


EID: 84969953705     PISSN: 21646376     EISSN: 21646414     Source Type: Journal    
DOI: 10.5890/DNC.2014.09.008     Document Type: Article
Times cited : (5)

References (86)
  • 2
    • 0038718854 scopus 로고    scopus 로고
    • The structure and function of complex networks
    • Newman, M.E.J. (2003), The structure and function of complex networks, SIAM Review, 45, 167-256
    • (2003) SIAM Review , vol.45 , pp. 167-256
    • Newman, M.E.J.1
  • 5
    • 0032482432 scopus 로고    scopus 로고
    • Collective dynamics of 'small-world' networks
    • Watts, D.J. and Strogatz, S.H. (1998), Collective dynamics of 'small-world' networks, Nature, 393, 440-442
    • (1998) Nature , vol.393 , pp. 440-442
    • Watts, D.J.1    Strogatz, S.H.2
  • 6
    • 0038483826 scopus 로고    scopus 로고
    • Emergence of scaling in random networks
    • Barabási, A.-L. and Albert, R.(1999), Emergence of scaling in random networks, Science, 286, 509-512
    • (1999) Science , vol.286 , pp. 509-512
    • Barabási, A.-L.1    Albert, R.2
  • 9
    • 67650732919 scopus 로고    scopus 로고
    • Reply to the comment on 'monte carlo simulation study of the two-stage percolation transition in enhanced binary trees'
    • Nogawa, T. and Hasegawa, T. (2009), Reply to the comment on 'monte carlo simulation study of the two-stage percolation transition in enhanced binary trees', Journal of Physics A: Mathematical and Theoretical, 42, 478002
    • (2009) Journal of Physics A: Mathematical and Theoretical , vol.42
    • Nogawa, T.1    Hasegawa, T.2
  • 10
    • 77952415088 scopus 로고    scopus 로고
    • Critical phase of bond percolation on growing networks
    • Hasegawa, T. and Nemoto, K. (2010), Critical phase of bond percolation on growing networks. Physical Review E, 81, 051105
    • (2010) Physical Review E , vol.81
    • Hasegawa, T.1    Nemoto, K.2
  • 11
    • 78651298909 scopus 로고    scopus 로고
    • Generating-function approach for bond percolation in hierarchical networks
    • Hasegawa, T., Sato, M., and Nemoto, K. (2010), Generating-function approach for bond percolation in hierarchical networks, Physical Review E, 82, 046101
    • (2010) Physical Review E , vol.82
    • Hasegawa, T.1    Sato, M.2    Nemoto, K.3
  • 12
    • 84862689463 scopus 로고    scopus 로고
    • Generalized scaling theory for critical phenomena including essential singularities and infinite dimensionality
    • Nogawa, T., Hasegawa, T., and Nemoto, K. (2012), Generalized scaling theory for critical phenomena including essential singularities and infinite dimensionality, Physical Review Letters, 108, 255703
    • (2012) Physical Review Letters , vol.108
    • Nogawa, T.1    Hasegawa, T.2    Nemoto, K.3
  • 13
    • 84866379231 scopus 로고    scopus 로고
    • Criticality governed by the stable renormalization fixed point of the ising model in the hierarchical small-world network
    • Nogawa, T., Hasegawa, T., and Nemoto, K. (2012), Criticality governed by the stable renormalization fixed point of the ising model in the hierarchical small-world network, Physical Review E, 86, 030102
    • (2012) Physical Review E , vol.86
    • Nogawa, T.1    Hasegawa, T.2    Nemoto, K.3
  • 14
    • 84875524695 scopus 로고    scopus 로고
    • Absence of the nonpercolating phase for percolation on the nonplanar hanoi network
    • Hasegawa, T. and Nogawa, T. (2013), Absence of the nonpercolating phase for percolation on the nonplanar hanoi network, Physical Review E, 87, 032810
    • (2013) Physical Review E , vol.87
    • Hasegawa, T.1    Nogawa, T.2
  • 15
    • 84887850760 scopus 로고    scopus 로고
    • Profile and scaling of the fractal exponent of percolations in complex networks
    • Hasegawa, T., Nogawa, T., and Nemoto, K. (2013), Profile and scaling of the fractal exponent of percolations in complex networks, EPL (Europhysics Letters), 104, 16006
    • (2013) EPL (Europhysics Letters) , vol.104 , pp. 16006
    • Hasegawa, T.1    Nogawa, T.2    Nemoto, K.3
  • 19
    • 0034345423 scopus 로고    scopus 로고
    • Phase transitions on nonamenable graphs
    • R. Lyons. Phase transitions on nonamenable graphs. Journal of Mathematical Physics, 41:1099, 2000
    • Journal of Mathematical Physics , vol.41 , Issue.1099 , pp. 2000
    • Lyons, R.1
  • 20
    • 0035534947 scopus 로고    scopus 로고
    • Multiplicity of phase transitions and mean-field criticality on highly non-amenable graphs
    • Schonmann, R.H. (2001), Multiplicity of phase transitions and mean-field criticality on highly non-amenable graphs, Communications in Mathematical Physics, 219, 271-322
    • (2001) Communications in Mathematical Physics , vol.219 , pp. 271-322
    • Schonmann, R.H.1
  • 22
    • 38149143883 scopus 로고
    • Some relations between analytic and geometric properties of infinite graphs
    • Mohar, B. (1991), Some relations between analytic and geometric properties of infinite graphs,. Discrete mathematics, 95, 193-219
    • (1991) Discrete mathematics , vol.95 , pp. 193-219
    • Mohar, B.1
  • 24
    • 0035365355 scopus 로고    scopus 로고
    • Size-dependent degree distribution of a scale-free growing network
    • Dorogovtsev, S.N., Mendes, J.F.F., and Samukhin, A.N. (2001), Size-dependent degree distribution of a scale-free growing network. Physical Review E, 63, 062101
    • (2001) Physical Review E , vol.63
    • Dorogovtsev, S.N.1    Mendes, J.F.F.2    Samukhin, A.N.3
  • 25
    • 33846658223 scopus 로고
    • Cayley trees, the ising problem. and the thermodynamic limit
    • Eggarter, T.P. (1974), Cayley trees, the ising problem, and the thermodynamic limit. Physical Review B, 9, 2989
    • (1974) Physical Review B , vol.9 , pp. 2989
    • Eggarter, T.P.1
  • 27
    • 70749097536 scopus 로고    scopus 로고
    • Comment on 'monte carlo simulation study of the two-stage percolation transition in enhanced binary trees'
    • Baek, S. K., Minnhagen, P., and Kim, B.J. (2009), Comment on 'monte carlo simulation study of the two-stage percolation transition in enhanced binary trees', Journal of Physics A: Mathematical and Theoretical, 42, 478001
    • (2009) Journal of Physics A: Mathematical and Theoretical , vol.42
    • Baek, S.K.1    Minnhagen, P.2    Kim, B.J.3
  • 28
    • 77954822144 scopus 로고    scopus 로고
    • Analytic results for the percolation transitions of the enhanced binary tree
    • Minnhagen, P. and Baek, S.K. (2010), Analytic results for the percolation transitions of the enhanced binary tree, Physical Review E, 82, 011113
    • (2010) Physical Review E , vol.82
    • Minnhagen, P.1    Baek, S.K.2
  • 29
    • 84871768904 scopus 로고    scopus 로고
    • Crossing on hyperbolic lattices
    • Gu, H. and Ziff, R.M. (2012), Crossing on hyperbolic lattices, Physical Review E, 85, 051141
    • (2012) Physical Review E , vol.85
    • Gu, H.1    Ziff, R.M.2
  • 30
    • 84861939906 scopus 로고    scopus 로고
    • Upper transition point for percolation on the enhanced binary tree: A sharpened lower bound
    • Baek, S.K. (2012), Upper transition point for percolation on the enhanced binary tree: A sharpened lower bound, Physical Review E, 85, 051128
    • (2012) Physical Review E , vol.85
    • Baek, S.K.1
  • 32
    • 84871768161 scopus 로고    scopus 로고
    • Bounds of percolation thresholds on hyperbolic lattices
    • Lee, J.F. and Baek, S.K. (2012), Bounds of percolation thresholds on hyperbolic lattices, Physical Review E, 86, 062105
    • (2012) Physical Review E , vol.86
    • Lee, J.F.1    Baek, S.K.2
  • 33
    • 0034721164 scopus 로고    scopus 로고
    • Error and attack tolerance of complex networks
    • Albert, R., Jeong, H., and Barabási, A.-L. (2000), Error and attack tolerance of complex networks, Nature, 406, 378-382
    • (2000) Nature , vol.406 , pp. 378-382
    • Albert, R.1    Jeong, H.2    Barabási, A.-L.3
  • 35
    • 41349120185 scopus 로고    scopus 로고
    • Percolation critical exponents in scale-free networks
    • Cohen, R., ben Avraham, D., and Havlin, S. (2002), Percolation critical exponents in scale-free networks, Physical Review E, 66, 036113
    • (2002) Physical Review E , vol.66
    • Cohen, R.1    ben Avraham, D.2    Havlin, S.3
  • 36
    • 84990671447 scopus 로고
    • A critical point for random graphs with a given degree sequence
    • Molloy, M. and Reed, B. (1995), A critical point for random graphs with a given degree sequence, Random Structures & Algorithms, 6, 161-180
    • (1995) Random Structures & Algorithms , vol.6 , pp. 161-180
    • Molloy, M.1    Reed, B.2
  • 40
    • 84860538825 scopus 로고    scopus 로고
    • Robustness of onionlike correlated networks against targeted attacks
    • Tanizawa, T., Havlin, S., and Stanley, H.E. (2012), Robustness of onionlike correlated networks against targeted attacks, Physical Review E, 85, 046109
    • (2012) Physical Review E , vol.85
    • Tanizawa, T.1    Havlin, S.2    Stanley, H.E.3
  • 41
    • 42749099621 scopus 로고    scopus 로고
    • Properties of highly clustered networks
    • Newman, M.E.J., Properties of highly clustered networks, Physical Review E, 68, 026121
    • Physical Review E , vol.68
    • Newman, M.E.J.1
  • 42
    • 70349974267 scopus 로고    scopus 로고
    • Bond percolation on a class of clustered random networks
    • Gleeson, J.P. (2009), Bond percolation on a class of clustered random networks, Physical Review E, 80, 036107
    • (2009) Physical Review E , vol.80
    • Gleeson, J.P.1
  • 43
    • 70449411707 scopus 로고    scopus 로고
    • Analytical results for bond percolation and k-core sizes on clustered networks
    • Gleeson, J.P. and Melnik, S. (2009), Analytical results for bond percolation and k-core sizes on clustered networks Physical Review E, 80, 046121
    • (2009) Physical Review E , vol.80
    • Gleeson, J.P.1    Melnik, S.2
  • 44
    • 77953973695 scopus 로고    scopus 로고
    • How clustering affects the bond percolation threshold in complex networks
    • Gleeson, J.P., Melnik, S., and Hackett, A. (2010), How clustering affects the bond percolation threshold in complex networks, Physical Review E, 81, 066114
    • (2010) Physical Review E , vol.81
    • Gleeson, J.P.1    Melnik, S.2    Hackett, A.3
  • 48
    • 37649031137 scopus 로고    scopus 로고
    • Infinite-order percolation and giant fluctuations in a protein interaction network
    • Kim, J., Krapivsky, P.L., Kahng, B., and Redner, S.(2002), Infinite-order percolation and giant fluctuations in a protein interaction network, Physical Review E, 66, 055101
    • (2002) Physical Review E , vol.66
    • Kim, J.1    Krapivsky, P.L.2    Kahng, B.3    Redner, S.4
  • 53
    • 22144454306 scopus 로고    scopus 로고
    • The phase transition in the uniformly grown random graph has infinite order
    • Bollobás, B., Janson, S., and Riordan, O. (2005), The phase transition in the uniformly grown random graph has infinite order, Random Structures & Algorithms, 26, 1-36
    • (2005) Random Structures & Algorithms , vol.26 , pp. 1-36
    • Bollobás, B.1    Janson, S.2    Riordan, O.3
  • 54
    • 24144489044 scopus 로고    scopus 로고
    • Slow emergence of the giant component in the growing m-out graph
    • Bollobás, B. and Riordan, O. (2005), Slow emergence of the giant component in the growing m-out graph, Random Structures & Algorithms, 27, 1-24
    • (2005) Random Structures & Algorithms , vol.27 , pp. 1-24
    • Bollobás, B.1    Riordan, O.2
  • 55
    • 26844481982 scopus 로고    scopus 로고
    • The small giant component in scale-free random graphs
    • Riordan, O. (2005), The small giant component in scale-free random graphs, Combinatorics Probability and Computing, 14, 897-938
    • (2005) Combinatorics Probability and Computing , vol.14 , pp. 897-938
    • Riordan, O.1
  • 56
    • 33745044280 scopus 로고    scopus 로고
    • Derivation of the percolation threshold for the network model of barabási and albert
    • Pietsch, W. (2006), Derivation of the percolation threshold for the network model of barabási and albert, Physical Review E, 73, 066112
    • (2006) Physical Review E , vol.73
    • Pietsch, W.1
  • 62
    • 0038542979 scopus 로고    scopus 로고
    • Renormalization group for evolving networks
    • Dorogovtsev, S.N. (2003), Renormalization group for evolving networks, Physical Review E, 67, 045102
    • (2003) Physical Review E , vol.67
    • Dorogovtsev, S.N.1
  • 64
    • 34547311119 scopus 로고    scopus 로고
    • Percolation in hierarchical scale-free nets
    • Rozenfeld, H.D. and ben Avraham, D. (2007), Percolation in hierarchical scale-free nets, Physical Review E, 75, 061102
    • (2007) Physical Review E , vol.75
    • Rozenfeld, H.D.1    ben Avraham, D.2
  • 65
    • 33745669442 scopus 로고    scopus 로고
    • Inverted berezinskii-kosterlitz-thouless singularity and high-temperature algebraic order in an ising model on a scale-free hierarchical-lattice small-world network
    • Hinczewski, M. and Berker, A.N. (2006), Inverted berezinskii-kosterlitz-thouless singularity and high-temperature algebraic order in an ising model on a scale-free hierarchical-lattice small-world network, Physical Review E, 73, 066126
    • (2006) Physical Review E , vol.73
    • Hinczewski, M.1    Berker, A.N.2
  • 66
    • 70350528567 scopus 로고    scopus 로고
    • Critical percolation phase and thermal berezinskii-kosterlitzthouless transition in a scale-free network with short-range and long-range random bonds
    • Berker, A.N., Hinczewski, M., and Netz, R.R. (2009), Critical percolation phase and thermal berezinskii-kosterlitzthouless transition in a scale-free network with short-range and long-range random bonds, Physical Review E, 80, 041118
    • (2009) Physical Review E , vol.80
    • Berker, A.N.1    Hinczewski, M.2    Netz, R.R.3
  • 67
    • 84860313558 scopus 로고    scopus 로고
    • Ordinary percolation with discontinuous transitions
    • Boettcher, S., Singh, V., and Ziff, R. M. (2012), Ordinary percolation with discontinuous transitions. Nature Communications, 3, 787
    • (2012) Nature Communications , vol.3 , pp. 787
    • Boettcher, S.1    Singh, V.2    Ziff, R.M.3
  • 68
    • 79151476279 scopus 로고    scopus 로고
    • Farey graphs as models for complex networks
    • Zhang, Z. and Comellas, F. (2011), Farey graphs as models for complex networks,. Theoretical Computer Science, 412(8), 865-875
    • (2011) Theoretical Computer Science , vol.412 , Issue.8 , pp. 865-875
    • Zhang, Z.1    Comellas, F.2
  • 69
    • 70350247587 scopus 로고    scopus 로고
    • Patchy percolation on a hierarchical network with small-world bonds
    • Boettcher, S., Cook, J.L., and Ziff, R.M. (2009), Patchy percolation on a hierarchical network with small-world bonds, Physical Review E, 80, 041115
    • (2009) Physical Review E , vol.80
    • Boettcher, S.1    Cook, J.L.2    Ziff, R.M.3
  • 70
    • 34547345211 scopus 로고    scopus 로고
    • Finite-size scaling in complex networks
    • Hong, H., Ha, M., and Park, H. (2007), Finite-size scaling in complex networks, Physical Review Letters, 98, 258701
    • (2007) Physical Review Letters , vol.98
    • Hong, H.1    Ha, M.2    Park, H.3
  • 71
    • 0039862319 scopus 로고    scopus 로고
    • Ising models on hyperbolic graphs
    • Wu, C.C. (1996), Ising models on hyperbolic graphs, Journal of statistical physics, 85, 251-259
    • (1996) Journal of statistical physics , vol.85 , pp. 251-259
    • Wu, C.C.1
  • 72
    • 0034343872 scopus 로고    scopus 로고
    • Ising models on hyperbolic graphs ii
    • Wu, C.C. (2000), Ising models on hyperbolic graphs ii, Journal of Statistical Physics, 100, 893-904
    • (2000) Journal of Statistical Physics , vol.100 , pp. 893-904
    • Wu, C.C.1
  • 75
    • 68949174093 scopus 로고    scopus 로고
    • Survival of short-range order in the ising model on negatively curved surfaces
    • Sakaniwa, Y. and Shima, H. (2009), Survival of short-range order in the ising model on negatively curved surfaces. Physical Review E, 80, 021103
    • (2009) Physical Review E , vol.80
    • Sakaniwa, Y.1    Shima, H.2
  • 76
    • 34547893018 scopus 로고    scopus 로고
    • Corner transfer matrix renormalization group method applied to the ising model on the hyperbolic plane
    • Ueda, K., Krcmar, R., Gendiar, A., and Nishino, T. (2007), Corner transfer matrix renormalization group method applied to the ising model on the hyperbolic plane, Journal of the Physical Society of Japan, 76, 084004
    • (2007) Journal of the Physical Society of Japan , vol.76
    • Ueda, K.1    Krcmar, R.2    Gendiar, A.3    Nishino, T.4
  • 77
  • 79
    • 84864591349 scopus 로고    scopus 로고
    • Weak correlation effects in the ising model on triangular-tiled hyperbolic lattices
    • Gendiar, A., Krcmar, R., Andergassen, S., Daniška, M., and Nishino, T. (2012), Weak correlation effects in the ising model on triangular-tiled hyperbolic lattices, Physical Review E, 86, 021105
    • (2012) Physical Review E , vol.86
    • Gendiar, A.1    Krcmar, R.2    Andergassen, S.3    Daniška, M.4    Nishino, T.5
  • 80
    • 33244495092 scopus 로고    scopus 로고
    • Phase transition with the berezinskii-kosterlitz-thouless singularity in the ising model on a growing network
    • Bauer, M., Coulomb, S. and Dorogovtsev, S.N. (2005), Phase transition with the berezinskii-kosterlitz-thouless singularity in the ising model on a growing network, Physical Review Letters, 94, 200602
    • (2005) Physical Review Letters , vol.94
    • Bauer, M.1    Coulomb, S.2    Dorogovtsev, S.N.3
  • 81
    • 79952505756 scopus 로고    scopus 로고
    • Fixed-point properties of the ising ferromagnet on the hanoi networks
    • Boettcher, S., and Brunson, C.T. (2011), Fixed-point properties of the ising ferromagnet on the hanoi networks. Physical Review E, 83, 021103
    • (2011) Physical Review E , vol.83
    • Boettcher, S.1    Brunson, C.T.2
  • 82
    • 84866145991 scopus 로고    scopus 로고
    • Renormalization group for critical phenomena in complex networks
    • Boettcher, S. and Brunson, C.T. (2011), Renormalization group for critical phenomena in complex networks. Frontiers in Physiology, 2
    • (2011) Frontiers in Physiology , pp. 2
    • Boettcher, S.1    Brunson, C.T.2
  • 83
    • 85041332077 scopus 로고    scopus 로고
    • Classification of critical phenomena having a parameter-dependent renormalization
    • Boettcher, S. and Brunson, C.T. (2012), Classification of critical phenomena having a parameter-dependent renormalization, arXiv:1209.3447
    • (2012)
    • Boettcher, S.1    Brunson, C.T.2
  • 84
  • 85
    • 0030371517 scopus 로고    scopus 로고
    • Multiple transition points for the contact process on the binary tree
    • Liggett, T.M. (1996), Multiple transition points for the contact process on the binary tree, The Annals of Probability, 24(4), 1675-1710
    • (1996) The Annals of Probability , vol.24 , Issue.4 , pp. 1675-1710
    • Liggett, T.M.1
  • 86
    • 0030360082 scopus 로고    scopus 로고
    • The existence of an intermediate phase for the contact process on trees
    • Stacey, A.M. (1996), The existence of an intermediate phase for the contact process on trees, The Annals of Probability, 1711-1726
    • (1996) The Annals of Probability , pp. 1711-1726
    • Stacey, A.M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.