Directed random dot product graphs

Internet Mathematics

Volumn 5, Issue 1-2, 2008, Pages 91-111

  Young, Stephen J ^a   Scheinerman, Edward ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b Johns Hopkins University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84924125330     PISSN: 15427951     EISSN: None     Source Type: Journal    
DOI: 10.1080/15427951.2008.10129301     Document Type: Article

References (24)

1. Milton Abramowitz and Irene A. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series 55. Washington, DC: U.S. Government Printing Office, 1964.
2. Dimitris Achlioptas, David Kempe, Aaron Clasuet, and Christopher Moore. “On the Bias of Traceroute Sampling or, Power-Law Degree Distributions in Regular Graphs.” In Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing, pp. 694–703. New York: ACM Press, 2005.
3. Réka Albert and Albert-László Barabási. “Statistical Mechanics of Complex Networks.” Rev. Modern Phys. 74:1 (2002), 47–97.
4. Yossi Azar, Amos Fiat, Anna Karlin, Frank McSherry, and Jared Saia. “Spectral Analysis of Data.” In Proceedings of the 33rd ACM Symposium on Theory of Computing, pp. 619–626. New York: ACM Press, 2001.
5. Aharon Ben-Tal and Arkadi Nemirovski. Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications. Philadelphia: SIAM, 2001.
6. Béla Bollobás. Modern Graph Theory, Graduate Texts in Mathematics 184. New York: Springer, 1998.
7. Stefan Bornholdt and Heinz Georg Schuster, editors. Handbook of Graphs and Networks. Weinheim: Wiley-VCH, 2003.
8. G. Caldarelli, A. Capocci, P. de Los Rios, and M. A. Muñoz. “Scale-Free Networks from Varying Vertex Intrinsic Fitness.” Physical Review Letters 89:25 (2002), 258702.
9. Fan Chung, David J. Galas, T. Gregory Dewey, and Lincoln Lu. “Duplication Models for Biological Networks.” Journal of Computational Biology 10:5 (2003), 677–687.
10. Rick Durrett. Random Graph Dynamics, Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge, UK: Cambridge University Press, 2007.
11. Stephen Eubank, V. S. Anil Kumar, Madhav V. Marathe, Aravind Srinivasan, and Nan Wang. “Structural and Algorithmic Aspects of Massive Social Networks.” In Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms, pp. 718–727. Philadelphia: SIAM, 2004.
12. Abraham D. Flaxman, Alan M. Frieze, and Juan Vera. “A Geometric Preferential Attachment Model of Networks.” Internet Math. 3:2 (2006), 187–205.
13. Christos Gkantsidis, Milena Mihail, and Amin Saberi. “Hybrid Search Schemes for Unstructured Peer-to-Peer Networks.” INFOCOM2005, Proceedings IEEE 3:13–17 (2005), 1526–1537.
14. Geoffrey R. Grimmett and David R. Stirzaker. Probability and Random Processes, third edition. New York: Oxford University Press, 2001.
15. Jon M. Kleinberg. “The Small World Phenomenon: An Algorithmic Perspective.” In Proceedings of the Thirty-Second Annual ACM Symposium on the Theory of Computing, pp. 163–170. New York: ACM Press, 1999.
16. Miro Kraetzl, Christine Nickel, and Edward R. Scheinerman. “Random Dot Product Graphs: A Model for Social Networks.” Manuscript, 2005.
17. Miro Kraetzl, Christine Nickel, Edward R. Scheinerman, and Kimberly Tucker. “Random Dot Product Graphs.” Available at http://www.ipam.ucla.edu/abstract.aspx?tid=5498, 2005.
18. Ravi Kumar, Prabhakar Raghavan, Sridhar Rajagopalan, D. Sivakumar, Andrew Tompkins, and Eli Upfal. “The Web as a Graph.” In Proceedings of the 19th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, pp. 1–10. New York: ACM Press, 2000.
19. Anukool Lakhina, John W. Byers, Mark Crovella, and Peng Xie. “Sampling Biases in IP Topology Measurements.” In INFOCOM 2003: Twenty- Second Annual Joint Conference of the IEEE Computer and Communications Societies, Vol. 1, pp 332–341. Los Alamitos, CA: IEEE Press, 2003.
20. Jure Leskovec, Jon Kleinberg, and Christos Faloutsos. “Graph Evolution: Densification and Shrinking Diameters.” ACM Trans. Knowl. Discov. Data 1:1 (2007), Article No. 2.
21. Milena Mihail, Amin Saberi, and Prasad Tetali. “Random Walks with Lookahead in Power Law Random Graphs.” Internet Mathematics 3:2 (2006), 147–152.
22. Milena Mihail, Christos Papadimitriou, and Amin Saberi. “On Certain Connectivity Properties of the Internet Topology.” J. Comput. System Sci. 72:2 (2006), 239–251.
23. M. E. J. Newman. “Assortative Mixing in Networks.” Physical Review Letters 89:20 (2002), 208701.
24. Nico M. Temme. “Large Parameter Cases of the Gauss Hypergeometric Function.” In Proceedings of the Sixth International Symposium on Orthogonal Polynomials, Special Functions and Their Applications, Journal of Computational and Applied Mathematics 153:1–5 (2003), 441–462.