Random Walks on Deterministic Weighted Scale-Free Small-World Networks with a Perfect Trap

Random walks are the most fundamental process among various dynamical processes, and most previous works focused on binary networks. This work studies random walks on deterministic weighted scale-free small-world networks with a perfect trap. We derive an explicit expression of the mean first passage time on the network with a trap. Meanwhile, we present the evolutionary rule for the first passage time when the network grows. The study can be useful for understanding the random walks on weighted networks.