  Random walks are a fundamental tool for analyzing realistic complex networked
systems and implementing randomized algorithms to solve diverse problems such
as searching and sampling. For many real applications, their actual effect and
convenience depend on the properties (e.g. stationary distribution and hitting
time) of random walks, with biased random walks often outperforming traditional
unbiased random walks (TURW). In this paper, we present a new class of biased
random walks, non-backtracking centrality based random walks (NBCRW) on a
network, where the walker prefers to jump to neighbors with high
non-backtracking centrality that has some advantages over eigenvector
centrality. We study some properties of the non-backtracking matrix of a
network, on the basis of which we propose a theoretical framework for fast
computation of the transition probabilities, stationary distribution, and
hitting times for NBCRW on the network. Within the paradigm, we study NBCRW on
some model and real networks and compare the results with those corresponding
to TURW and maximal entropy random walks (MERW), with the latter being biased
random walks based on eigenvector centrality. We show that the behaviors of
stationary distribution and hitting times for NBCRW widely differ from those
associated with TURW and MERW, especially for heterogeneous networks.
