Construction and Analysis of Random Networks with Explosive Percolation
Abstract
The existence of explosive phase transitions in random (Erd os R\'enyi-type) networks has been recently documented by Achlioptas et al.\ [Science 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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