Biased random walks in the scale-free networks with the disassortative degree correlation

Random walk has been applied to exploring the effective transport strategy of data package in complex networks. Because the disassortative degree correlation is ubiquitous in technical networks including the internet, we study the biased random walks in the scale-free networks with the disassortative degree correlation. Computer simulation shows that the degree correlation changes the behavior of the random walk. Random walkers are located on small degree nodes with a low probability, and they can be distributed homogeneously on other nodes. We find out the optimal biased coefficient that ensures the most homogeneous distribution on large nodes. In the optimal case, the degree-correlated network exhibits a more efficient random walk than degree-uncorrelated networks. We propose the mechanism for the effect of the disassortative mixing on the random walk.