Universality for the distance in finite variance random graphs

Journal of Statistical Physics

Volumn 133, Issue 1, 2008, Pages 169-202

  Van Den Esker, Henri ^a   Van Der Hofstad, Remco ^b   Hooghiemstra, Gerard ^a  

^a Department of Microelectronics   (Netherlands)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Branching processes; Coupling; Graph distances; Inhomogeneous random graphs; Random Graphs; Universality

Indexed keywords

EID: 52149087216     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-008-9594-z     Document Type: Article

References (21)

1. Asmussen, S.: Some martingale methods in the limit theory of supercritical branching processes. In: Branching Processes. Advances in Probability and related Topics, pp. 1-26 (1978)
2. E.A. Bender E.R. Canfield 1978 The asymptotic number of labelled graphs with given degree sequences J. Comb. Theory A 24 3 296 307
3. Bollobás, B.: Random Graphs. Cambridge University Press, Cambridge (2001)
4. Bollobás, B., Borgs, C., Chayes, J.T., Riordan, O.: Directed scale-free graphs. In: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 132-139 (2003)
5. B. Bollobás S. Janson O. Riordan 2007 The phase transition in inhomogeneous random graphs Random Struct. Algorithms 31 1 3 122
6. T. Britton M. Deijfen A. Martin-Löf 2006 Generating simple random graphs with prescribed degree distribution J. Stat. Phys. 124 6 1377 1397
7. F. Chung L. Lu 2002 The average distances in random graphs with expected degrees Proc Natl. Acad. Sci. 99 25 15879 15882
8. F. Chung L. Lu 2002 Connected components in random graphs with given expected degree sequences Ann. Comb. 6 2 125 145
9. van den Esker, H., van der Hofstad, R., Hooghiemstra, G.: Universality for the distance in finite variance random graphs: extended version. http://arxiv.org/abs/math.PR/0605414
10. H. van den Esker R. van der Hofstad G. Hooghiemstra D. Znamenski 2006 Distances in random graphs with infinite mean degrees Extremes 8 111 140
11. Feller, W.: An Introduction to Probability Theory and Its Applications, vol. II, 2nd edn. Wiley, New York (1971)
12. Gut, A.: Probability: A Graduate Course. Springer, Berlin (2005)
13. R. van der Hofstad G. Hooghiemstra P. Van Mieghem 2005 Distances in random graphs with finite variance degrees Random Struct. Algorithms 27 2 76 123
14. R. van der Hofstad G. Hooghiemstra D. Znamenski 2007 Distances in random graphs with finite mean and infinite variance degrees Electron. J. Probab. 12 703 766
15. Janson, S.: Asymptotic equivalence and contiguity of some random graphs. Preprint (2008)
16. Janson, S., Luczak, T., Ruciński, A.: Random Graphs. Wiley, New York (2000)
17. Molloy, M., Reed, B.: A critical point for random graphs with a given degree sequence. In: Proceedings of the Sixth International Seminar on Random Graphs and Probabilistic Methods in Combinatorics and Computer Science, pp. 161-179 (1995)
18. M.E.J. Newman S.H. Strogatz D.J. Watts 2001 Random graphs with arbitrary degree distribution and their application Phys. Rev. E 64 026118
19. I. Norros H. Reittu 2004 On the power-law random graph model of massive data networks Perform. Eval. 55 1-2 3 23
20. I. Norros H. Reittu 2006 On a conditionally Poissonian graph process Adv. Appl. Probab. 38 1 59 75
21. Thorisson, H.: Coupling, Stationarity and Regeneration. Springer, Berlin (2000)