110
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Growth of common friends in a preferential attachment model

ORCID Icon &
Pages 427-447 | Received 26 Jun 2020, Accepted 26 Mar 2021, Published online: 20 Apr 2021

References

  • Abramowitz, M.; Stegun, I. A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards Applied Mathematics Series 55. U.S. Government Printing Office, Washington, D.C., 1964.
  • Adamic, L. A.; Adar, E. Friends and Neighbors on the Web. Social Netw. 2003, 25, 211–230. DOI: 10.1016/S0378-8733(03)00009-1.
  • Backstrom, L.; Boldi, P.; Rosa, M.; Ugander, J.; Vigna, S. Four Degrees of Separation. Proceedings of the 4th Annual ACM Web Science Conference. WebSci '12 . Association for Computing Machinery, New York, NY, USA, 2012; pp. 33–42.
  • Barabási, A.; Albert, R. Emergence of Scaling in Random networks. Science 1999, 286, 509–512. DOI: 10.1126/science.286.5439.509.
  • Barabási, A.; Jeong, H.; Néda, Z.; Ravasz, E.; Schubert, A.; Vicsek, T. Evolution of the Social Network of Scientific Collaborations. Phys. A. 2002, 311, 590–614. DOI: 10.1016/S0378-4371(02)00736-7.
  • Bloznelis, M.; Kurauskas, V. Clustering Function: Another View on Clustering Coefficient. J. Complex. Netw. 2016, 4, 61–86. DOI: 10.1093/comnet/cnv010.
  • Bollobás, B.; Borgs, C.; Chayes, J.; Riordan, O. Directed Scale-Free Graphs. Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms (Baltimore, 2003), 2003; pp. 132–139.
  • Bollobás, B.; Riordan, O.; Spencer, J.; Tusnády, G. The Degree Sequence of a Scale-Free Random Graph Process. Random Struct. Alg. 2001, 18, 279–290. DOI: 10.1002/rsa.1009.
  • Cooper, C.; Frieze, A. A General Model of Web Graphs. Random Struct. Alg. 2003, 22, 311–335. DOI: 10.1002/rsa.10084.
  • Dereich, S.; Mörters, P. Random Networks with Sublinear Preferential Attachment: Degree Evolutions. Electron. J. Probab. 2009, 14, 1222–1267. DOI: 10.1214/EJP.v14-647.
  • Durrett, R. T. Probability: Theory and Examples. Cambridge Series in Statistical and Probabilistic Mathematics, 5th ed.; Cambridge University Press: Cambridge, 2019; Vol. 49.
  • Elwes, R. A Preferential Attachment Process Approaching the Rado Graph. Proc. Edinb. Math. Soc. 2020, 63, 443–455. DOI: 10.1017/S0013091519000336.
  • Gupta, P.; Goel, A.; Lin, J.; Sharma, A.; Wang, D.; Zadeh, R. WTF: The Who to Follow Service at Twitter. Proceedings of the 22nd International Conference on World Wide Web. WWW '13. ACM: New York, NY, USA, 2013, pp. 505–514.
  • Liben-Nowell, D.; Kleinberg, J. The Link-Prediction Problem for Social Networks. J. Am. Soc. Inf. Sci. 2007, 58, 1019–1031. DOI: 10.1002/asi.20591.
  • Myers, S. A.; Sharma, A.; Gupta, P.; Lin, J. Information Network or Social Network? The Structure of the Twitter Follow Graph. Proceedings of the 23rd International Conference on World Wide Web. WWW ’14 Companion. Association for Computing Machinery, New York, NY, USA, 2014; pp. 493–498.
  • Newman, M. E. Clustering and Preferential Attachment in Growing Networks. Phys. Rev. E. Stat. Nonlin. Soft Matter Phys. 2001, 64, 025102. DOI: 10.1103/PhysRevE.64.025102.
  • Resnick, S. I.; Samorodnitsky, G. Tauberian Theory for Multivariate Regularly Varying Distributions with Application to Preferential Attachment Networks. Extremes 2015, 18, 349–367. DOI: 10.1007/s10687-015-0216-2.
  • Rosenthal, H. P. On the Subspaces of Lp (p > 2) Spanned by Sequences of Independent Random Variables. Israel J. Math. 1970, 8, 273–303. DOI: 10.1007/BF02771562.
  • Samorodnitsky, G.; Resnick, S.; Towsley, D.; Davis, R.; Willis, A.; Wan, P. Nonstandard Regular Variation of in-Degree and out-Degree in the Preferential Attachment Model. J. Appl. Probab. 2016, 53, 146–161. DOI: 10.1017/jpr.2015.15.
  • van der Hofstad, R. Random Graphs and Complex Networks. Vol. 1. Cambridge Series in Statistical and Probabilistic Mathematics, [43]. Cambridge University Press: Cambridge, 2017.
  • Wan, P.; Wang, T.; Davis, R. A.; Resnick, S. I. Fitting the Linear Preferential Attachment Model. Electron. J. Stat. 2017, 11, 3738–3780.
  • Wang, T.; Resnick, S. I. Consistency of Hill Estimators in a Linear Preferential Attachment Model. Extremes 2019, 22, 1–28. DOI: 10.1007/s10687-018-0335-7.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.