Modeling the small-world phenomenon with local network flow

Internet Mathematics

Volumn 2, Issue 3, 2005, Pages 359-385

  Andersen, Reid ^a   Chung, Fan ^a   Lu, Linyuan ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38049054223     PISSN: 15427951     EISSN: None     Source Type: Journal    
DOI: 10.1080/15427951.2005.10129109     Document Type: Article

References (30)

1. L. A. Adamic and B. A. Huberman. “Growth Dynamics of the World Wide Web.” Nature 401 (September 9, 1999), 131.
2. W. Aiello, F. Chung and L. Lu. “A Random Graph Model for Massive Graphs.” In Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, pp. 171–180. New York: ACM Press, 2000.
3. R. B. R. Azevedo and A. M. Leroi. “A Power Law for Cells.” Proc. Natl. Acad. Sci. USA 98:10 (2001), 5699–5704.
4. Georg Baier. “Flows with Path Restrictions.” PhD thesis, Technische Universität Berlin, 2003.
5. A.-L. Barabási and Réka Albert. “Emergence of Scaling in Random Networks.” Science 286 (1999), 509–512.
6. A. Barabási, R. Albert, and H. Jeong. “Scale-Free Characteristics of Random Networks: The Topology of the World Wide Web.” Physica A 272 (1999), 173–187.
7. B. Bollobás. Random Graphs. New York: Academic Press, 1985.
8. S. Boyles and G. Exoo. “A Counterexample to a Conjecture on Paths of Bounded Length.” J. Graph Theory 6 (1982), 205–209.
9. A. Broder, R. Kumar, F. Maghoul, P. Raghavan, S. Rajagopalan, R. Stata, A. Tompkins, and J. Wiener. “Graph Structure in theWeb.” Presented at WWW9 Conference, May, 2000, Amsterdam. Paper version appeared in Computer Networks 33:1–6 (2000), 309–321.
10. K. Calvert, M. Doar, and E. Zegura. “Modeling Internet Topology.” IEEE Communications Magazine 35:6 (1997), 160–163.
11. F. Chung and L. Lu. “Average Distances in Random Graphs with Given Expected Degree Sequences.” Proceedings of National Academy of Science 99 (2002), 15879–15882.
12. Fan Chung and Linyuan Lu. “Connected Components in a Random Graph with Given Degree Sequences.” Annals of Combinatorics 6 (2002), 125–145.
13. F. Chung and L. Lu. “The Small World Phenomenon in Hybrid Power Law Graphs.” In Complex Networks, edited by Eli Ben-Naim, Hans Frauenfelder and Zoltan Toroczkai, pp. 91–106, Lecture Notes in Physics 650. Berlin: Springer-Verlag, 2004.
14. C. Cooper and A. Frieze. “On a General Model of Web Graphs.” Random Structures and Algorithms 22 (2003), 311–335.
15. M. Faloutsos, P. Faloutsos, and C. Faloutsos. “On Power-Law Relationships of the Internet Topology.” In Proceedings of the Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, pp. 251–262. New York: ACM Press, 1999.
16. P. Erdős and T. Gallai. “Gráfok elő´ırt fokú pontokkal” (Graphs with points of prescribed degrees, in Hungarian). Mat. Lapok 11 (1961), 264–274.
17. G. W. Flake, R. E. Tarjan and K. Tsioutsiouliklis. “Graph Clustering and Minimum Cut Trees.” Internet Math. 1:4 (2004), 385–408.
18. N. Garg and J. Könemann. “Faster and Simpler Algorithms for Multicommodity Flow and Other Fractional Packing Problems.” Technical Report, Max-Planck-Institut fur Informatik, Saarbrucken, Germany, 1997.
19. A. Itai, Y. Perl, and Y. Shiloach. “The Complexity of Finding Maximum Disjoint Paths with Length Constraints.” Networks 12 (1982), 277–286.
20. S. Jain and S. Krishna. “A Model for the Emergence of Cooperation, Interdependence, and Structure in Evolving Networks.” Proc. Natl. Acad. Sci. USA 98:2 (2001), 543–547.
21. J. Kleinberg. “The Small-World Phenomenon: An Algorithmic Perspective.” In Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing, pp. 163–170. New York: ACM Press, 2000.
22. S. R. Kumar, P. Raghavan, S. Rajagopalan and A. Tomkins. “Extracting Large-Scale Knowledge Bases from the Web.” In Proceedings of the 25th International Conference on Very Large Data Bases, pp. 639–650. San Francisco: Morgan Kaufmann, 1999.
23. R. Kumar, P. Raghavan, S. Rajagopalan, D. Sivakumar, A. Tomkins and E. Upfal. “Stochastic Models for the Web Graph.” Proceedings of the 41st Annual Symposium on Foundations of Computer Science, pp. 57–65. Los Alamitos, CA: IEEE Press, 2000.
24. R. Kumar, P. Raghavan, S. Rajagopalan, D. Sivakumar, A. Tomkins, and E. Upfal. “The Web as a Graph.” In Proceedings of the Nineteenth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pp. 1–10. New York: ACM Press, 2000.
25. L. Lovász, V. Neumann-Lara, and M. Plummer. “Mengerian Theorems for Paths of Bounded Length.” Periodica Mathematica Hungarica 9 (1978), pp. 269–276.
26. M. Mitzenmacher. “A Brief History of Generative Models for Power Law and Lognormal Distributions.” Internet Math. 1:2 (2003), 226–251.
27. M. E. J Newman. “The Structure of Scientific Collaboration Networks.” Proc. Natl. Acad. Sci. USA 98:2 (2001), 404–409.
28. S. Plotkin, D. B. Shmoys, and E. Tardos. “Fast Approximation Algorithms for Fractional Packing and Covering Problems.” Mathematics of Operations Research 20 (1995), 257–301.
29. D. J. Watts and S. H. Strogatz. “Collective Dynamics of ‘Small-World’ Networks.” Nature 393 (1998), 440–442.
30. Neal E. Young. “Randomized Rounding without Solving the Linear Program.” In Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 170–178. Philadelphia, PA: SIAM, 1995.