Random hyperbolic graphs: Degree sequence and clustering (extended abstract)

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 7392 LNCS, Issue PART 2, 2012, Pages 573-585

  Gugelmann, Luca ^a   Panagiotou, Konstantinos ^b   Peter, Ueli ^a  

^a ETH ZURICH   (Switzerland)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATA THEORY; MAXIMUM LIKELIHOOD; ROBOTS;

ASYMPTOTIC EXPRESSIONS; CLUSTERING COEFFICIENT; DEGREE DISTRIBUTIONS; EXTENDED ABSTRACTS; HYPERBOLIC GEOMETRY; MATHEMATICAL ANALYSIS; POWER LAW DISTRIBUTION; RANDOM GEOMETRIC GRAPHS;

GRAPHIC METHODS;

EID: 84884175645     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-31585-5_51     Document Type: Conference Paper

References (21)

1. Aiello, W., Chung, F., Lu, L.: Random evolution in massive graphs. In: Proceedings of the 42nd IEEE Symposium on Foundations of Computer Science, pp. 510-519. IEEE (2001)
2. Anderson, J.W.: Hyperbolic geometry, 2nd edn. Springer (2005)
3. Barab́asi, A.L., Albert, R.: Emergence of Scaling in Random Networks. Science 286(5439), 509-512 (1999)
4. Bollob́as, B., Riordan, O., Spencer, J., Tusńady, G.: The degree sequence of a scale-free random graph process. Random Structures and Algorithms 18(3), 279-290 (2001)
5. Bollob́as, B., Riordan, O.: Mathematical results on scale-free random graphs. In: Handbook of Graphs and Networks, pp. 1-34 (2002)
6. Borgs, C., Chayes, J., Daskalakis, C., Roch, S.: First to market is not everything: an analysis of preferential attachment with fitness. In: Proceedings of the 39th ACM Symposium on Theory of Computing, pp. 135-144. ACM (2007)
7. Buckley, P., Osthus, D.: Popularity based random graph models leading to a scalefree degree sequence. Discrete Mathematics 282(1-3), 53-68 (2004)
8. Chierichetti, F., Kumar, R., Lattanzi, S., Panconesi, A., Raghavan, P.: Models for the compressible web. In: Proceedings of the 50th IEEE Symposium on Foundations of Computer Science, pp. 331-340. IEEE (2009)
9. Cooper, C., Frieze, A.: A general model of web graphs. Random Structures & Algorithms 22(3), 311-335 (2003)
10. Dubhashi, D., Panconesi, A., Press, C.U.: Concentration of measure for the analysis of randomized algorithms. Cambridge University Press (2009)
11. Faloutsos, M., Faloutsos, P., Faloutsos, C.: On power-law relationships of the internet topology. ACM SIGCOMM Computer Communication Review 29, 251-262 (1999)
12. Krioukov, D., Papadopoulos, F., Kitsak, M., Vahdat, A., Boguñ́a, M.: Hyperbolic Geometry of Complex Networks. Physical Review E 82(3) (2010)
13. Lattanzi, S., Sivakumar, D.: Affiliation networks. In: Proceedings of the 41st ACM Symposium on Theory of Computing, pp. 427-434. ACM (2009)
14. Leskovec, J., Kleinberg, J., Faloutsos, C.: Graphs over time: densification laws, shrinking diameters and possible explanations. In: Proceedings of the 11th ACM SIGKDD International Conference on Knowledge Discovery in Data Mining, pp. 177-187. ACM (2005)
15. Milgram, S.: The small world problem. Psychology Today 2(1), 60-67 (1967)
16. Mitzenmacher, M.: A brief history of generative models for power law and lognormal distributions. Internet Mathematics 1(2), 226-251 (2004)
17. Newman, M., Park, J.: Why social networks are different from other types of networks. Physical Review E 68(3), 036122 (2003)
18. Papadopoulos, F., Krioukov, D., Boguñ́a, M., Vahdat, A.: Greedy forwarding in dynamic scale-free networks embedded in hyperbolic metric spaces. In: Proceedings of the 29th IEEE International Conference on Computer Communications, INFOCOM 2010, pp. 2973-2981 (2010)
19. Serrano, M., Boguñ́a, M.: Clustering in complex networks. i. general formalism. Physical Review E 74(5), 056114 (2006)
20. Travers, J., Milgram, S.: An experimental study of the small world problem. Sociometry, 425-443 (1969)
21. Watts, D.J., Strogatz, S.H.: Collective dynamics of small-world networks. Nature 393(6684), 440-442 (1998)