Mean first-passage times for two biased walks on the weighted rose networks

Abstract

Compared with traditional random walk, biased walks have been studied extensively over the past decade especially in the transport and communication networks. In this paper, we first introduce the weighted rose networks. Then, for the weighted rose networks we focus on two biased walks, maximal entropy walk and weight-dependent walk, and obtain the exact expressions of their stationary distributions and mean first-passage times. Finally, we find that the average receiving time for maximal entropy walk is a quadratic function of the weight parameter r while the average receiving time for weighted-dependent walk is a linear function of the weight parameter r. Meanwhile, for the maximal entropy walk, the smaller the value of r is, the more efficient the trapping process is. For the weighted-dependent walk, the larger the value of r(r<r0≈2.6) is, the more efficient for the weighted-dependent walk, the smaller the value of r(r>r0≈2.6) is, the more efficient for the weight-dependent walk.