TY - GEN

T1 - Distance in the forest fire model how far are you from Eve?

AU - Kanade, Varun

AU - Levi, Reut

AU - Lotker, Zvi

AU - Mallmann-Trenn, Prederik

AU - Mathieu, Claire

N1 - Publisher Copyright:
© (2016) by SIAM: Society for Industrial and Applied Mathematics.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - Leskovec, Kleinberg and Faloutsos (2005) observed that many social networks exhibit properties such as shrinking (i.e. bounded) diameter, densification, and (power-law) heavy tail degree distributions. To explain these phenomena, they introduced a generative model, called the Forest Fire model, and using simulations showed that this model indeed exhibited these properties; however, proving this rigorously was left as an open problem. In this paper, we analyse one of these properties, shrinking diameter. We define a restricted version of their model that incorporates the main features that seem to contribute towards this property, and prove that the graphs generated by this model exhibit shrinking distance to the seed graph. We prove that an even simpler model, the random walk model, already exhibits this phenomenon.

AB - Leskovec, Kleinberg and Faloutsos (2005) observed that many social networks exhibit properties such as shrinking (i.e. bounded) diameter, densification, and (power-law) heavy tail degree distributions. To explain these phenomena, they introduced a generative model, called the Forest Fire model, and using simulations showed that this model indeed exhibited these properties; however, proving this rigorously was left as an open problem. In this paper, we analyse one of these properties, shrinking diameter. We define a restricted version of their model that incorporates the main features that seem to contribute towards this property, and prove that the graphs generated by this model exhibit shrinking distance to the seed graph. We prove that an even simpler model, the random walk model, already exhibits this phenomenon.

UR - http://www.scopus.com/inward/record.url?scp=84963525732&partnerID=8YFLogxK

U2 - 10.1137/1.9781611974331.ch109

DO - 10.1137/1.9781611974331.ch109

M3 - Conference contribution

AN - SCOPUS:84963525732

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 1602

EP - 1620

BT - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016

A2 - Krauthgamer, Robert

PB - Association for Computing Machinery

T2 - 27th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016

Y2 - 10 January 2016 through 12 January 2016

ER -