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arXiv · 1203.0299

Criticality and Continuity of Explosive Site Percolation in Random Networks

J. H. Qian·D. D. Han·Y. G. Ma
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Abstract

This Letter studies the critical point as well as the discontinuity of a class of explosive site percolation in Erdös and Rényi (ER) random network. The class of the percolation is implemented by introducing a best-of-m rule. Two major results are found: i). For any specific $m$, the critical percolation point scales with the average degree of the network while its exponent associated with $m$ is bounded by -1 and $\sim-0.5$. ii). Discontinuous percolation could occur on sparse networks if and only if $m$ approaches infinite. These results not only generalize some conclusions of ordinary percolation but also provide new insights to the network robustness.

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J. H. Qian, D. D. Han, Y. G. Ma. 2012-12-03. Criticality and Continuity of Explosive Site Percolation in Random Networks. https://doi.org/10.1209/0295-5075%2F100%2F48006

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