Random intersection graphs with tunable degree distribution and clustering

Probability in the Engineering and Informational Sciences

Volumn 23, Issue 4, 2009, Pages 661-674

  Deijfen, Maria ^a   Kets, Willemien ^b,c  

^a STOCKHOLM UNIVERSITY   (Sweden)

^b SANTA FE INSTITUTE   (United States)

^c TILBURG UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC EXPRESSIONS; DEGREE DISTRIBUTIONS; POWER-LAW; RANDOM INTERSECTION GRAPHS; RANDOM WEIGHT; WEIGHT DISTRIBUTIONS;

GRAPH THEORY;

EID: 75049085976     PISSN: 02699648     EISSN: 14698951     Source Type: Journal    
DOI: 10.1017/S0269964809990064     Document Type: Article

References (20)

1. Bollobás, B., Janson, S., & Riordan, O. (2007). The phase transition in inhomogeneous random graphs. Random Structures & Algorithms 31: 3-122.
2. Britton, T., Deijfen, M.,Lagerås, A., &Lindholm, M. (2008). Epidemics on random graphs with tunable clustering. Journal of Applied Probability 45: 743-756.
3. Britton, T., Deijfen, M., & Martin-Löf, A. (2006). Generating simple random graphs with prescribed degree distribution. Journal of Statistical Physics 124: 1377-1397.
4. Chung, F. & Lu. L (2002). Connected components in random graphs with given degree sequences. Annals ofCombinatorics 6: 125-145.
5. Chung, F. & Lu. L (2002). The average distances in random graphs with given expected degrees. Proceedings of the National Academy of Sciences, USA 99: 15,879-15,882.
6. Deijfen, M., van den Esker, H., van den Hofstad, R., & Hooghiemstra, G. (2009). A preferential attachment model with random initial degrees. Arkiv för Matematik 47: 41-72.
7. Dorogovtsev, S. & Mendes, J. (2003). Evolution of networks, from biological nets to the Internet and WWW. Oxford: Oxford University Press.
8. Fill, J., Scheinerman, E., & Singer-Cohen, K. (2000). Random intersection graphs when m ω(n):An equivalence theorem relating the evolution of the G(n, m, p) and G(n, p) models. Random Structures & Algorithms 16: 156-176.
9. Godehardt, E. & Jaworski, J. (2002). Two models of random intersection graphs for classification. In M. Schwaiger & O. Opitz (eds.), Exploratory data analysis in empirical research. New York: Springer, pp. 67-81.
10. Jaworski, J., Karoński, M., & Stark, D. (2006). The degree of a typical vertex in generalized random intersection graph models. Discrete Mathematics 306: 2152-2165.
11. Karoński, M., Scheinerman, E., & Singer-Cohen, K. (1999). On random intersection graphs: The subgraphs problem. Combinatorics, Probability & Computing 8: 131-159.
12. Molloy, M., & Reed, B. (1995). A critical point for random graphs with a given degree sequence. Random Structures & Algorithms 6: 161-179.
13. Molloy, M., & Reed, B. (1998). The size of the giant component of a random graph with a given degree sequence. Combinatorics, Probability & Computing 7: 295-305.
14. Newman, M. E. J. (2003). Properties of highly clustered networks. Physical Review E 68: 026121.
15. Newman, M. E. J. & Park, J. (2003). Why social networks are different from other types of networks. Physical Review E 68: 036122.
16. Newman, M. E. J., Strogatz, S. H., & Watts, D. J. (2002). Random graphs with arbitrary degree distributions and their applications. Physical Review E 64: 026118.
17. Palla, G., Derényi, I., Farkas, I., & Vicsek, T. (2005). Uncovering the overlapping community structure of complex networks in nature and society. Nature 435: 814-818.
18. Singer, K. (1995). Random intersection graphs, Ph.D. thesis, Johns Hopkins University. Baltimore, MD.
19. Stark, D. (2004). The vertex degree distribution of random intersection graphs. Random Structures & Algorithms 24: 249-258.
20. Yao, X., Zhang, C., Chen, J., & Li, Y. (2005). On the scale-free intersection graphs. Lecture Notes in Computer Science No. 3481. Berlin: Springer, pp. 1217-1224.