Explosive percolation transitions in growing networks

Abstract

Recent extensive studies of the explosive percolation (EP) model revealed that the EP transition is of second order with extremely small value of the order parameter exponent beta. This result was obtained from static random networks, in which the number of nodes in the system remains constant during the evolution of the network. However, on-line social networks, where the giant component among the members grows quickly, can be growing networks, in which the number of nodes in the system is increased with time steps. Thus, one needs to study EP transitions occurring in growing networks. Here we study a general case in which the number of node candidates that are selected at each time step is given as m. When m=2, this model reduces to an existing model that is the ordinary percolation model in growing networks, which undergoes an infinite-order transition. When m >= 3, however, we find that the transition becomes second order due to the suppression effect against the growth of large clusters. Using the rate equation approach and Monte Carlo simulations, we show that the exponent beta decreases algebraically with increasing m, whereas it decreases exponentially for static networks.