Lazy random walks on the weighted pseudofractal scale-free networks with a perfect trap

This paper investigates the average trapping time problem of particles performing lazy random walks on a weighted scale-free pseudofractal network. We introduced three different parameters, namely, the weight r of the edge during iteration, the probability p of particles jumping at the old node position, and the probability q of particles jumping at the new node position. By analyzing the behavior of particles at different node positions, the analytical expression for the average trapping time was obtained. Based on the analytical expression, numerical simulation graph is drawn for different parameters, and the results showed that particles using lazy random walks can improve transmission efficiency.