Random Networks with Concave Preferential Attachment Rule

Jahresbericht der Deutschen Mathematiker-Vereinigung

Volumn 113, Issue 1, 2011, Pages 21-40

  Dereich, Steffen ^a   Mörters, Peter ^b  

^a PHILIPPS UNIVERSITY MARBURG   (Germany)

^b University of Bath   (United Kingdom)

Author keywords

Barabasi Albert model; Cluster; Dynamic random graph; Giant component; Graph distance; Maximal degree; Multitype branching random walk; Nonlinear preferential attachment; Scale free network

Indexed keywords

EID: 84872078509     PISSN: 00120456     EISSN: 18697135     Source Type: Journal    
DOI: 10.1365/s13291-010-0011-6     Document Type: Article

References (23)

1. Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999) DOI: 10.1126/science.286.5439.509
2. Bender, E.A., Canfield, E.R.: The asymptotic number of labelled graphs with a given degree sequence. J. Comb. Theory 24, 296–307 (1978) DOI: 10.1016/0097-3165(78)90059-6
3. Bollobás, B., Riordan, O.: Robustness and vulnerability of scale-free random graphs. Internet Math. 1, 1–35 (2003)
4. Bollobás, B., Riordan, O.: The diameter of a scale-free random graph. Combinatorica 24, 5–34 (2004) DOI: 10.1007/s00493-004-0002-2
5. Bollobás, B., Riordan, O., Spencer, J., Tusnády, G.: The degree sequence of a scale-free random graph process. Random Struct. Algorithms 18, 279–290 (2001) DOI: 10.1002/rsa.1009
6. Chung, F., Lu, L.: The average distances in random graphs with given expected degrees. Proc. Natl. Acad. Sci. USA 99, 15879–15882 (2002) DOI: 10.1073/pnas.252631999
7. Dommers, S., van der Hofstad, R., Hooghiemstra, G.: Diameters in preferential attachment models. J. Stat. Phys. 139, 72–107 (2010) DOI: 10.1007/s10955-010-9921-z
8. Dereich, S., Mörters, P.: Random networks with sublinear preferential attachment: degree evolutions. Electron. J. Probab. 14, 1222–1267 (2009)
9. Dereich, S., Mörters, P.: Random networks with sublinear preferential attachment: the giant component. arXiv:1007.0899 (2010)
10. Dereich, S., Mönch, C., Mörters, P.: Typical distances in ultrasmall random networks (2010, in preparation)
11. Dereich, S., Mönch, C., Mörters, P.: Random networks with sublinear preferential attachment: small worlds (2011, in preparation)
12. Katona, Z., Móri, T.F.: A new class of scale free random graphs. Stat. Probab. Lett. 76, 1587–1593 (2006) DOI: 10.1016/j.spl.2006.04.017
13. Krapivsky, P.L., Redner, S., Leyvraz, F.: Connectivity of growing random networks. Phys. Rev. Lett. 85, 4629 (2000) DOI: 10.1103/PhysRevLett.85.4629
14. Móri, T.F.: On random trees. Studia Sci. Math. Hung. 39, 143–155 (2002)
15. Oliveira, R., Spencer, J.: Connectivity transitions in networks with super-linear preferential attachment. Internet Math. 2, 121–163 (2005)
16. Rudas, A., Tóth, B., Valkó, B.: Random trees and general branching processes. Random Struct. Algorithms 31, 186–202 (2007) DOI: 10.1002/rsa.20137
17. Singer, K.B.: Random intersection graphs. Ph.D. thesis, Johns Hopkins University (1995)
18. Stark, D.: The vertex degree distribution of random intersection graphs. Random Struct. Algorithms 24, 249–258 (2004) DOI: 10.1002/rsa.20005
19. Team, N.W.B.: Network workbench tool. Indiana University, Northeastern University, and University of Michigan, page http://nwb.slis.indiana.edu (2006)
20. van der Hofstad, R.: Random graphs and complex networks. In: Lecture Notes, Eindhoven (2009)
21. van der Hofstad, R., Hooghiemstra, G., van Mieghem, P.: Distances in random graphs with finite variance degrees. Random Struct. Algorithms 27, 76–123 (2005) DOI: 10.1002/rsa.20063
22. van der Hofstad, R., Hooghiemstra, G., Znamenski, D.: Distances in random graphs with finite mean and infinite variance degrees. Electron. J. Probab. 12, 703–766 (2007)
23. Watts, D.J., Strogatz, S.H.: Collective dynamics of ‘small-world’ networks. Nature 393, 440–442 (1998) DOI: 10.1038/30918