Average trapping time on a half 3-level nested network

Abstract In this paper, we focus on a half nested network ( HS n ∘ N ), which is the left half of nested network ( S n ∘ N ) based on the vertical cutting of symmetry axis. We study the capture problem of unbiased random walk on HS n ∘ N . Further, the change in diffusion efficiency between HS n ∘ N and S n ∘ N is studied. According to the self-similarity of the network, the analytical expression of the average trapping time of HS n ∘ N is obtained. In addition, we draw the relevant numerical simulation diagram. By comparing the growth trend of the two curves, we find that with the increase of the number of network iterations, the average trapping time of HS n ∘ N does not change much compared with S n ∘ N . It indicates that the diffusion efficiency of the network after vertical cutting is not affected much at large scale.