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A giant cluster emerges discontinuously in bond percolation in variousnetworks when the growth of large clusters is globally suppressed. It wasrecently revealed that this phenomenon occurs even in a scale-free (SF)network, where hubs accelerate the growth of large clusters. The SF networkused in the previous study was disassortative, though, so it is necessary tocheck whether the phenomenon also occurs in an assortative SF network, whereeach hub prefers to be connected to another hub and thus the large clustergrowth is accelerated. In this paper, we find that the phenomenon, namely thediscontinuous emergence of a giant cluster in bond percolation with the globalsuppression of large clusters, also occurs in an assortative SF network.Interestingly, the generated network is also assortative but not a SF networkat the transition point, unlike the disassortative SF network generated at thetransition point in the previous study. We observe similar behaviors in twoadditional models and discuss the results.

Discontinuous emergence of a giant cluster in assortative scale-free networks