Construction and Analysis of Random Networks with Explosive Percolation

Details Construction and Analysis of Random Networks with Explosive Percolation Construction and Analysis of Random Networks with Explosive Percolation

2009-10-20

arxiv.org/abs/0910.3979v2

Phys. Rev. Let. 103, 255701 (2009)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

The existence of explosive phase transitions in random (Erd\H os R\'enyi-type) networks has been recently documented by Achlioptas et al.\ [Science {\bf 323}, 1453 (2009)] via simulations. In this Letter we describe the underlying mechanism behind these first-order phase transitions and develop tools that allow us to identify (and predict) when a random network will exhibit an explosive transition. Several interesting new models displaying explosive transitions are also presented.

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