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A first-order percolation transition, called explosive percolation, was recently discovered in evolution networks with random edge selection under a certain restriction. However, the network percolation with more realistic evolution mechanisms such as preferential attachment has not yet been concerned. We propose a tunable network percolation model by introducing a hybrid mechanism of edge selection into the Bohman-Frieze-Wormald model, in which a parameter adjusts the relative weights between random and preferential selections. A large number of simulations indicate that there exist crossover phenomena of percolation transition by adjusting the parameter in the evolution processes. When the strategy of selecting a candidate edge is dominated by random selection, a single discontinuous percolation transition occurs. When a candidate edge is selected more preferentially based on nodes degree, the size of the largest component undergoes multiple discontinuous jumps, which exhibits a peculiar difference from the network percolation of random selection with a certain restriction. Besides, the percolation transition becomes continuous when the candidate edge is selected completely preferentially.
Heterogeneous adoption thresholds exist widely in social contagions, but were always neglected in previous studies. We first propose a non-Markovian spreading threshold model with general adoption threshold distribution. In order to understand the ef
In this article we presented a brief study of the main network models with growth and preferential attachment. Such models are interesting because they present several characteristics of real systems. We started with the classical model proposed by B
In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under attacks. I
Social network is a main tunnel of rumor spreading. Previous studies are concentrated on a static rumor spreading. The content of the rumor is invariable during the whole spreading process. Indeed, the rumor evolves constantly in its spreading proces
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