title: Construction and analysis of random networks with explosive percolation.
abstract: The existence of explosive phase transitions in random (Erdös Rényi-type) networks has been recently documented by Achlioptas, D'Souza, and Spencer [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.
authors.affiliation: School of ORIE and Center for Applied Mathematics, Cornell University, Ithaca, New York 14850, USA.
authors.forename: Eric J
authors.initials: EJ
authors.lastname: Friedman
authors.forename: Adam S
authors.initials: AS
authors.lastname: Landsberg