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Volumn 40, Issue 6, 2012, Pages 2299-2361

Novel scaling limits for critical inhomogeneous random graphs

Author keywords

Critical random graphs; Inhomogeneous networks; Multiplicative coalescent; Phase transitions; Thinned L vy processes

Indexed keywords


EID: 84872586705     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/11-AOP680     Document Type: Article
Times cited : (70)

References (36)
  • 1
    • 0036013593 scopus 로고    scopus 로고
    • Statistical mechanics of complex networks
    • ALBERT, R. and BARABÁSI, A.-L. (2002). Statistical mechanics of complex networks. Rev. Modern Phys. 74 47-97. MR1895096
    • (2002) Rev. Modern Phys , vol.74 , pp. 47-97
    • Albert, R.1    Barabási, A.-L.2
  • 2
    • 0031483018 scopus 로고    scopus 로고
    • Brownian excursions, critical random graphs and the multiplicative coalescent
    • ALDOUS, D. (1997). Brownian excursions, critical random graphs and the multiplicative coalescent. Ann. Probab. 25 812-854. MR1434128
    • (1997) Ann. Probab , vol.25 , pp. 812-854
    • Aldous, D.1
  • 3
    • 0003300947 scopus 로고    scopus 로고
    • The entrance boundary of the multiplicative coalescent
    • (electronic).
    • ALDOUS, D. and LIMIC, V. (1998). The entrance boundary of the multiplicative coalescent. Electron. J. Probab. 3 59 pp. (electronic). MR1491528
    • (1998) Electron. J. Probab , vol.3 , pp. 59
    • Aldous, D.1    Limic, V.2
  • 4
    • 0001796185 scopus 로고    scopus 로고
    • Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists
    • ALDOUS, D. J. (1999). Deterministic and stochastic models for coalescence (aggregation and coagulation): A review of the mean-field theory for probabilists. Bernoulli 5 3-48. MR1673235
    • (1999) Bernoulli 5 3-48. MR1673235
    • Aldous, D.J.1
  • 5
    • 0003430191 scopus 로고    scopus 로고
    • Wiley, New York. With an appendix on the life and work of Paul Erdos.
    • ALON, N. and SPENCER, J. H. (2000). The Probabilistic Method, 2nd ed. Wiley, New York. With an appendix on the life and work of Paul Erd?os. MR1885388
    • (2000) The Probabilistic Method, 2nd ed
    • Alon, N.1    Spencer, J.H.2
  • 7
    • 33846526778 scopus 로고    scopus 로고
    • Random Fragmentation and Coagulation Processes
    • Cambridge Univ. Press, Cambridge.
    • BERTOIN, J. (2006). Random Fragmentation and Coagulation Processes. Cambridge Studies in Advanced Mathematics 102. Cambridge Univ. Press, Cambridge. MR2253162
    • (2006) Cambridge Studies in Advanced Mathematics 102
    • Bertoin, J.1
  • 8
    • 78649718778 scopus 로고    scopus 로고
    • Scaling limits for critical inhomogeneous random graphs with finite third moments
    • BHAMIDI, S., VAN DER HOFSTAD, R. and VAN LEEUWAARDEN, J. S. H. (2010). Scaling limits for critical inhomogeneous random graphs with finite third moments. Electron. J. Probab. 15 1682-1703. MR2735378
    • (2010) Electron. J. Probab. , vol.15 , pp. 1682-1703
    • Bhamidi, S.1    Van der Hofstad, R.2    Van Leeuwaarden, J.S.H.3
  • 12
    • 33750091606 scopus 로고    scopus 로고
    • Generating simple random graphs with prescribed degree distribution
    • BRITTON, T., DEIJFEN, M. andMARTIN-LÖF, A. (2006). Generating simple random graphs with prescribed degree distribution. J. Stat. Phys. 124 1377-1397. MR2266448
    • (2006) J. Stat. Phys. , vol.124 , pp. 1377-1397
    • Britton, T.1    Deijfen, M.2    Martin-LöF, A.3
  • 13
    • 0037058980 scopus 로고    scopus 로고
    • The average distances in random graphs with given expected degrees
    • (electronic).
    • CHUNG, F. and LU, L. (2002). The average distances in random graphs with given expected degrees. Proc. Natl. Acad. Sci. USA 99 15879-15882 (electronic). MR1944974
    • (2002) Proc. Natl. Acad. Sci. USA , vol.99 , pp. 15879-15882
    • Chung, F.1    Lu, L.2
  • 14
    • 0038763983 scopus 로고    scopus 로고
    • Connected components in random graphs with given expected degree sequences
    • CHUNG, F. and LU, L. (2002). Connected components in random graphs with given expected degree sequences. Ann. Comb. 6 125-145. MR1955514
    • (2002) Ann. Comb. , vol.6 , pp. 125-145
    • Chung, F.1    Lu, L.2
  • 15
    • 84906264352 scopus 로고    scopus 로고
    • The average distance in a random graph with given expected degrees
    • CHUNG, F. and LU, L. (2003). The average distance in a random graph with given expected degrees. Internet Math. 1 91-113. MR2076728
    • (2003) Internet Math. , vol.1 , pp. 91-113
    • Chung, F.1    Lu, L.2
  • 16
    • 53749101794 scopus 로고    scopus 로고
    • Complex Graphs and Networks
    • Conference Board of the Mathematical Sciences, Washington, DC.
    • CHUNG, F. and LU, L. (2006). Complex Graphs and Networks. CBMS Regional Conference Series in Mathematics 107. Conference Board of the Mathematical Sciences, Washington, DC. MR2248695
    • (2006) CBMS Regional Conference Series in Mathematics 107
    • Chung, F.1    Lu, L.2
  • 17
    • 34249008722 scopus 로고    scopus 로고
    • The volume of the giant component of a random graph with given expected degrees
    • (electronic).
    • CHUNG, F. and LU, L. (2006). The volume of the giant component of a random graph with given expected degrees. SIAM J. Discrete Math. 20 395-411 (electronic). MR2257269
    • (2006) SIAM J. Discrete Math. , vol.20 , pp. 395-411
    • Chung, F.1    Lu, L.2
  • 19
    • 84929729015 scopus 로고    scopus 로고
    • Cambridge Univ. Press, Cambridge.
    • DURRETT, R. (2007). Random Graph Dynamics. Cambridge Univ. Press, Cambridge. MR2271734
    • (2007) Random Graph Dynamics
    • Durrett, R.1
  • 24
    • 52949121797 scopus 로고    scopus 로고
    • The largest component in a subcritical random graph with a power law degree distribution
    • JANSON, S. (2008). The largest component in a subcritical random graph with a power law degree distribution. Ann. Appl. Probab. 18 1651-1668. MR2434185
    • (2008) Ann. Appl. Probab. , vol.18 , pp. 1651-1668
    • Janson, S.1
  • 25
    • 70749107400 scopus 로고    scopus 로고
    • Asymptotic equivalence and contiguity of some random graphs
    • JANSON, S. (2010). Asymptotic equivalence and contiguity of some random graphs. Random Structures Algorithms 36 26-45. MR2591045
    • (2010) Random Structures Algorithms , vol.36 , pp. 26-45
    • Janson, S.1
  • 27
    • 84872544300 scopus 로고    scopus 로고
    • The component sizes of a critical random graph with pre-described degree sequence
    • Preprint.
    • JOSEPH, A. (2010). The component sizes of a critical random graph with pre-described degree sequence. Preprint.
    • (2010)
    • Joseph, A.1
  • 30
    • 0038718854 scopus 로고    scopus 로고
    • The structure and function of complex networks
    • (electronic)
    • NEWMAN, M. E. J. (2003). The structure and function of complex networks. SIAM Rev. 45 167-256 (electronic). MR2010377
    • (2003) SIAM Rev , vol.45 , pp. 167-256
    • Newman, M.E.J.1
  • 31
    • 33646150930 scopus 로고    scopus 로고
    • On a conditionally Poissonian graph process
    • NORROS, I. and REITTU, H. (2006). On a conditionally Poissonian graph process. Adv. in Appl. Probab. 38 59-75. MR2213964
    • (2006) Adv. in Appl. Probab , vol.38 , pp. 59-75
    • Norros, I.1    Reittu, H.2
  • 32
    • 0004176142 scopus 로고    scopus 로고
    • Coupling, Stationarity, and Regeneration
    • Springer, New York
    • THORISSON, H. (2000). Coupling, Stationarity, and Regeneration. Springer, New York. MR1741181
    • (2000)
    • Thorisson, H.1
  • 34
    • 84872539961 scopus 로고    scopus 로고
    • Critical behavior in inhomogeneous random graphs
    • VAN DER HOFSTAD, R. (2009). Critical behavior in inhomogeneous random graphs. Preprint.
    • (2009) Preprint.
    • Van Der Hofstad, R.1
  • 35
    • 67651251708 scopus 로고    scopus 로고
    • Random graphs and complex networks
    • Available at
    • VAN DER HOFSTAD, R. (2011). Random graphs and complex networks. Unpublished manuscript. Available at http://www.win.tue.nl/~rhofstad/NotesRGCN.pdf.
    • (2011) Unpublished manuscript
    • Van der Hofstad, R.1
  • 36
    • 84872550367 scopus 로고    scopus 로고
    • The near-critical behavior for the configuration model with finite-variance degrees
    • Unpublished manuscript
    • VAN DER HOFSTAD, R., JANSON, S. and LUCZAK, M. The near-critical behavior for the configuration model with finite-variance degrees. Unpublished manuscript.
    • Van der Hofstad, R.1    Janson, S.2    Luczak, M.3


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