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Volumn 77, Issue 3, 2008, Pages

Laplacian spectra of, and random walks on, complex networks: Are scale-free architectures really important?

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; PARAMETER ESTIMATION; PROBLEM SOLVING; RANDOM PROCESSES; SIGNAL PROCESSING; WAVE PROPAGATION;

EID: 41149105343     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.036115     Document Type: Article
Times cited : (94)

References (37)
  • 1
    • 34548452165 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.99.098701
    • V. Sood and P. Grassberger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.098701 99, 098701 (2007).
    • (2007) Phys. Rev. Lett. , vol.99 , pp. 098701
    • Sood, V.1    Grassberger, P.2
  • 2
    • 34249656813 scopus 로고    scopus 로고
    • NJOPFM 1367-2630 10.1088/1367-2630/9/5/154
    • B. Kujawski, B. Tadić, and G. J. Rodgers, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/5/154 9, 154 (2007).
    • (2007) New J. Phys. , vol.9 , pp. 154
    • Kujawski, B.1    Tadić, B.2    Rodgers, G.J.3
  • 3
    • 0001714858 scopus 로고
    • PRBMDO 0163-1829 10.1103/PhysRevB.38.11461
    • A. J. Bray and G. J. Rodgers, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.38.11461 38, 11461 (1988).
    • (1988) Phys. Rev. B , vol.38 , pp. 11461
    • Bray, A.J.1    Rodgers, G.J.2
  • 4
    • 41149130067 scopus 로고    scopus 로고
    • A. Jamakovic and P. Van Mieghem, Proceedings of the European Conference on complex systems (ECCS'06), 2006, http://complexsystems.lri.fr/FinalReview/ FILES/PDF/p42.pdf
    • (2006)
    • Jamakovic, A.1    Van Mieghem, P.2
  • 7
    • 0001216057 scopus 로고
    • edited by Y. Alavari, G. Chartrand, O. R. Oellermann, and A. J. Schwenk (Wiley, New York
    • B. Mohar, in Graph Theory, Combinatorics and Applications, edited by, Y. Alavari, G. Chartrand, O. R. Oellermann, and, A. J. Schwenk, (Wiley, New York, 1991), Vol. 2, pp. 871-898.
    • (1991) Graph Theory, Combinatorics and Applications , vol.2 , pp. 871-898
    • Mohar, B.1
  • 8
    • 34547370524 scopus 로고    scopus 로고
    • CHAOEH 1054-1500 10.1063/1.2735019
    • D. Kim and B. Kahng, Chaos CHAOEH 1054-1500 10.1063/1.2735019 17, 026115 (2007).
    • (2007) Chaos , vol.17 , pp. 026115
    • Kim, D.1    Kahng, B.2
  • 9
    • 2542431567 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.92.144101
    • F. M. Atay, J. Jost, and A. Wende, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.144101 92, 144101 (2004).
    • (2004) Phys. Rev. Lett. , vol.92 , pp. 144101
    • Atay, F.M.1    Jost, J.2    Wende, A.3
  • 10
    • 34547310300 scopus 로고    scopus 로고
    • NJOPFM 1367-2630 10.1088/1367-2630/9/6/182
    • A. E. Motter, New J. Phys. NJOPFM 1367-2630 10.1088/1367-2630/9/6/182 9, 182 (2007).
    • (2007) New J. Phys. , vol.9 , pp. 182
    • Motter, A.E.1
  • 11
    • 42749102164 scopus 로고    scopus 로고
    • PLEEE8 1063-651X 10.1103/PhysRevE.69.036111
    • J. D. Noh and H. Rieger, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.69.036111 69, 036111 (2004).
    • (2004) Phys. Rev. e , vol.69 , pp. 036111
    • Noh, J.D.1    Rieger, H.2
  • 12
    • 2342616749 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.92.118701
    • J. D. Noh and H. Rieger, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.118701 92, 118701 (2004).
    • (2004) Phys. Rev. Lett. , vol.92 , pp. 118701
    • Noh, J.D.1    Rieger, H.2
  • 13
    • 41149158489 scopus 로고    scopus 로고
    • D. Aldous and J. Fill, Reversible Markov chains and random walks on graphs, 1999, http://www.stat.berkeley.edu/users/aldous/RWG/book.html
    • (1999)
    • Aldous, D.1    Fill, J.2
  • 14
    • 0036013593 scopus 로고    scopus 로고
    • RMPHAT 0034-6861 10.1103/RevModPhys.74.47
    • R. Albert and A.-L. Barabási, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.47 74, 47 (2002).
    • (2002) Rev. Mod. Phys. , vol.74 , pp. 47
    • Albert, R.1    Barabási, A.-L.2
  • 15
    • 0036610173 scopus 로고    scopus 로고
    • ADPHAH 0001-8732 10.1080/00018730110112519
    • S. N. Dorogovtsev and J. F. F. Mendes, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730110112519 51, 1079 (2002).
    • (2002) Adv. Phys. , vol.51 , pp. 1079
    • Dorogovtsev, S.N.1    Mendes, J.F.F.2
  • 17
    • 0038718854 scopus 로고    scopus 로고
    • SIREAD 0036-1445 10.1137/S003614450342480
    • M. E. J. Newman, SIAM Rev. SIREAD 0036-1445 10.1137/S003614450342480 45, 167 (2003).
    • (2003) SIAM Rev. , vol.45 , pp. 167
    • Newman, M.E.J.1
  • 24
    • 0000664045 scopus 로고
    • JCBTA7 0097-3165 10.1016/0097-3165(78)90059-6
    • E. A. Bender and E. R. Canfield, J. Comb. Theory, Ser. A JCBTA7 0097-3165 10.1016/0097-3165(78)90059-6 24, 296 (1978).
    • (1978) J. Comb. Theory, Ser. A , vol.24 , pp. 296
    • Bender, E.A.1    Canfield, E.R.2
  • 25
    • 0000755404 scopus 로고
    • JSTPBS 0022-4715 10.1007/BF01011791
    • B. D. Hughes and M. Sahimi, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01011791 29, 781 (1982).
    • (1982) J. Stat. Phys. , vol.29 , pp. 781
    • Hughes, B.D.1    Sahimi, M.2
  • 26
    • 84910818916 scopus 로고
    • EULEEJ 0295-5075 10.1209/0295-5075/9/7/003
    • D. Cassi, Europhys. Lett. EULEEJ 0295-5075 10.1209/0295-5075/9/7/003 9, 627 (1989).
    • (1989) Europhys. Lett. , vol.9 , pp. 627
    • Cassi, D.1
  • 27
    • 21844495721 scopus 로고
    • JPHAC5 0305-4470 10.1088/0305-4470/28/1/003
    • A. Giacometti, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/28/1/003 28, L13 (1995).
    • (1995) J. Phys. A , vol.28 , pp. 13
    • Giacometti, A.1
  • 28
    • 34547262756 scopus 로고    scopus 로고
    • PRLTAO 0031-9007 10.1103/PhysRevLett.98.248701
    • D.-H. Kim and A. E. Motter, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.248701 98, 248701 (2007).
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 248701
    • Kim, D.-H.1    Motter, A.E.2
  • 32
    • 41149163586 scopus 로고    scopus 로고
    • In fact, we applied a slightly different procedure. After step (i) we knew only the asymptotic of T (s,x) at Rex 1 and | s- sc | 1. The analytic continuation of T (s,x) as a function of the variable s to the area s< sc has a singularity in terms of the variable x at large x. Therefore, to calculate ρ (λ) at λ> λc, one can use 50. Then the asymptotics of ρ (λ) at λ→ λc +0 is defined by the position of the singularity with respect to the variable x, and by the behavior of T (-λ,x) near this singularity.
    • In fact, we applied a slightly different procedure. After step (i) we knew only the asymptotic of T (s,x) at Rex 1 and | s- sc | 1. The analytic continuation of T (s,x) as a function of the variable s to the area s< sc has a singularity in terms of the variable x at large x. Therefore, to calculate ρ (λ) at λ> λc, one can use 50. Then the asymptotics of ρ (λ) at λ→ λc +0 is defined by the position of the singularity with respect to the variable x, and by the behavior of T (-λ,x) near this singularity.
  • 33
    • 41149164092 scopus 로고    scopus 로고
    • Alternatively, find eigenfunctions and eigenvalues, ψm (s,x) and μm (s), of the integral equation 27. Then find P̄ l (s) by using Eqs. 31 32 33. Here the nontrivial part of the propagator, describing its relaxation to a stationary value, corresponds to the discrete part of the spectrum of characteristic numbers of this equation.
    • Alternatively, find eigenfunctions and eigenvalues, ψm (s,x) and μm (s), of the integral equation 27. Then find P̄ l (s) by using Eqs. 31 32 33. Here the nontrivial part of the propagator, describing its relaxation to a stationary value, corresponds to the discrete part of the spectrum of characteristic numbers of this equation.
  • 35
    • 0035420732 scopus 로고    scopus 로고
    • PLEEE8 1063-651X 10.1103/PhysRevE.64.026118
    • M. E. J. Newman, S. H. Strogatz, and D. J. Watts, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.64.026118 64, 026118 (2001).
    • (2001) Phys. Rev. e , vol.64 , pp. 026118
    • Newman, M.E.J.1    Strogatz, S.H.2    Watts, D.J.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.