How a complex network is connected crucially impacts its dynamics andfunction. Percolation, the transition to extensive connectedness upon gradualaddition of links, was long believed to be continuous but recent numericalevidence on "explosive percolation" suggests that it might as well bediscontinuous if links compete for addition. Here we analyze the microscopicmechanisms underlying discontinuous percolation processes and reveal a strongimpact of single link additions. We show that in generic competitivepercolation processes, including those displaying explosive percolation, singlelinks do not induce a discontinuous gap in the largest cluster size in thethermodynamic limit. Nevertheless, our results highlight that for large finitesystems single links may still induce observable gaps because gap sizes scaleweakly algebraically with system size. Several essentially macroscopic clusterscoexist immediately before the transition, thus announcing discontinuouspercolation. These results explain how single links may drastically changemacroscopic connectivity in networks where links add competitively.
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