Criticality and Continuity of Explosive Site Percolation in Random Networks

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.

5 pages, 5 figures

References in corpus (7)

• Critical phenomena in complex networks
• Self-organized adaptation of a simple neural circuit enables complex robot behaviour
• Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
• Explosive percolation in scale-free networks
• Explosive percolation via control of the largest cluster
• Strongly discontinuous explosive percolation with multiple giant components
• Tricritical point in explosive percolation