Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:B2L-A

Session:

Number:231

Detecting growth of groups in networks by using a transformation method from networks to time series

Yutaka Shimada,  Yoshito Hirata,  Tohru Ikeguchi,  Kazuyuki Aihara,  

pp.231-234

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.231

PDF download (1MB)

A novel framework to analyze nonlinear time series and complex networks has recently been proposed. In the framework, nonlinear time series are transformed to networks and analyzed through the transformed networks. On the other hand, the networks are also transformed to time series and analyzed through the obtained time series. In this paper, we show that the transformation method from the networks to the time series can be applied to analyze the evolution of sizes of communities in the networks. We apply the transformation method to an evolving network model and show that the method can detect the temporal change of the evolution of the citation network.

[1] Strogatz S.H. (2001) Nature 410:268-276; Albert R., Barabási A.-L. (2002) Rev. Mod. Phys. 74:47-97; Newman M.E.J. (2003) SIAM Rev. Soc. Ind. Appl. Math 45:167-256.

[2] Donner R. et al. (2010) New J. Phys. 12:033025.

[3] Zhang J. and Small M. (2006) Phys. Rev. Lett. 96:238701.

[4] Lacasa L. et al., (2008) Proc. Nat. Acad. Sci. USA 105:4972-4975.

[5] Shimada Y., Kimura T., and Ikeguchi T. (2008) Lect. Notes Comp. Sci. 5163:61-70.

[6] Shimada Y., and Ikeguchi T. (2010) Phys. Lett. A 374:3170-3176.

[7] Xu X., Zhang J., and Small M. (2008) Proc. Nat. Acad. Sci. USA 105:19601-19605.

[8] Marwan N. et al. (2009) Phys. Lett. A 373:4246-4254.

[9] Shimada Y., Ikeguchi T., and Shigehara T. (2012) Phys. Rev. Lett. 109:158701.

[10] Cox T.F. and Cox. M.A.A. (2000) Multidimensional Scaling, Chapman & Hall/CRC, Boca Raton, Florida.

[11] Klemm K. and Eguíluz V. (2002) Phys. Rev. E 65:057102.

[12] Newman M.E.J. (2006) Phys. Rev. E 74:036104.