Explosive Percolation in Random Networks

By Dimitris Achlioptas, Raissa M. D’Souza, Joel H. Spencer. Science, 2009

551 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3db608ac2263c69dfb9246a6eafda3c2f5cf15ff

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Catastrophic cascade of failures in interdependent networks (2009, background): “ is not the case, when interdependent systems are considered. Recently, several studies have been published, discussing how to change the stochastic rule of percolation to obtain an abrupt transition [27, 28, 29, 30, 31, 32] in a single network. When coupled interdependent systems are considered the”
The triangle-free process and R(3,k) (2013, background): “cularly well-studied processes include the `preferential attachment' models of Barabasi and Albert [7], and the socalled `Achlioptas processes' introduced by Achlioptas in 2000 (see, e.g., [2, 9, 11, 15, 50]), and studied most notably by Riordan and Warnke [45, 46]. We mention also the ver”
Self-organized adaptation of a simple neural circuit enables complex robot behaviour (2010, unknown): “Therefore, recent work by Achlioptas, D’Souza and Spence”
Robustness and resilience of complex networks (2024, background): “Among these, the most famous is the product rule that leads to explosive percolation 122 .”
Anomalous critical and supercritical phenomena in explosive percolation (2015, methodology): “ included in subsequent edges. Such arguments provide the intuition for why there is only one unique giant component in the supercritical regime for Erd˝os-R enyi percolation.´ The appearance of Ref. [16] led to increased activity in the ﬁeld and to the discovery of several random graph percolation ”
Recent advances in percolation theory and its applications (2015, background): “ble to shift the threshold. Moreover, the percolation transition is strongly conjectured to be continuous for all bounded-size rules [179]. For unbounded-size rules in contrast, extensive simulations [58] strongly suggested that, the product rule in particular, shows much more interesting behavior t”