Connectivity transitions in networks with super-linear preferential attachment

Internet Mathematics

Volumn 2, Issue 2, 2005, Pages 121-163

  Oliveira, Roberto ^a   Spencer, Joel ^b  

^a IBM T J WATSON RESEARCH CENTER   (United States)

^b NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 50249104858     PISSN: 15427951     EISSN: None     Source Type: Journal    
DOI: 10.1080/15427951.2005.10129101     Document Type: Article

References (20)

1. Réka Albert and Albert-László Barabási. “Statistical Mechanics of Complex Networks.” Reviews of Modern Physics 74 (2002), 47–97. Available at cond-mat/0106096.
2. Réka Albert, Haowoong Jeong, and Albert-László Barabási. “Diameter of the World Wide Web.” Nature 401 (1999), 130–131.
3. Noga Alon and Joel Spencer. The Probabilistic Method, Second edition. Wiley-Interscience Series in Discrete Mathematics and Optimization. New York: Wiley-Interscience, 2000.
4. Albert-László Barabási and Réka Albert. “Emergence of Scaling in Random Networks.” Science 286 (1999), 509–512.
5. Ginestra Bianconi and Albert-László Barabási. “Bose- Einstein Condensation in Complex Networks.” Physical Review Letters 86 (2001), 5632-5635.
6. Béla Bollobás and Oliver Riordan. “Mathematical Results on Scale-Free Random Graphs.” In Handbook of Graphs and Networks, edited by Stefan Burnholdt and Heinz Georg Schuster, pp. 1–34. Berlin: Wiley-VCH, 2003.
7. Béla Bollobás and Oliver Riordan. “Robustness and Vulnerability of Scale-Free Random Graphs.” Internet Mathematics 1:1 (2003), 1–35.
8. Béla Bollobás and Oliver Riordan. “The Diameter of a Scale-Free Random Graph.” Combinatorica 4 (2004), 5–34.
9. Béla Bollobás, Oliver Riordan, Joel Spencer, and Gábor Tárdos. “The Degree Sequence of a Scale-Free Random Graph Process.” Random Structures and Algorithms 18:3 (2000), 279–290.
10. Béla Bollobás, Christian Borgs, Jennifer Chayes, and Oliver Riordan. “Directed Scale-Free Graphs.” In Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 132–139. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2003.
11. Fan Chung, Shirin Handjani, and Doug Jungreis. “Generalizations of Pólya’s Urn Problem.” Annals of Combinatorics 7:2 (2003), 141–153.
12. Colin Cooper and Alan Frieze. “On a General Model of Web Graphs.” Random Structures and Algorithms 22 (2003), 311–335.
13. Burgess Davis. “Reinforced Random Walk.” Probability Theory and Related Fields 84:2 (1990), 203–229.
14. Serguei N. Dorogovtsev and José F. F. Mendes. “Evolution of Networks.” Advances in Physics 51 (2002), 1079–1187. Available at cond-mat/0106144.
15. Eleni Drinea, Mihaela Enachescu, and Michael Mitzenmacher. “Variations on Random Graph Models of the Web.” Harvard Technical Report TR-06- 01, 2001.
16. Eleni Drinea, Alan Frieze, and Michael Mitzenmacher. “Balls in Bins Models with Feedback.” In Proceedings of the Thirteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 308–315. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2002.
17. Kostya Khanin and Raya Khanin. “A Probabilistic Model for the Establishment of Neuron Polarity.” Journal of Mathematical Biology 42:1 (2001), 26–40.
18. P. L. Krapivsky and Sidney L. Redner. “Organization of Growing Random Networks.” Physics Reviews E 63 (2001), 066123-1–066123-14. Available at cond-mat/0011094.
19. Michael Mitzenmacher, Roberto Oliveira, and Joel Spencer. “A Scaling Result for Explosive Processes.” Electronic Journal of Combinatorics 11:1 (2004), R31.
20. Joel Spencer and Nicholas Wormald. Explosive Processes. Manuscript, 2004.