THE MEAN TRAPPING TIME ON THE TRUNCATED DIAMOND HIERARCHICAL NETWORK: THE EFFECT OF CUTTING MODES

Trapping problem is a fundamental problem to study random walk on complex networks and the mean trapping time (MTT) can be used to measure transmission efficiency of networks. Based on a classical diamond hierarchical network (DHN) with a trap, this paper studies the impact on the MTT of four cutting modes which are imposed on it. By the iterative relationship at two adjacent generations deduced by the structure of the truncated diamond hierarchical network (TDHN), we obtain the analytical expressions of MTTs on four truncated networks. The analytical results can be verified by the numerical results calculated by the matrix algorithm. The results show that, compared with the original untruncated network DHN, the four cuts obviously update the specific value of MTTs, but their scaling expressions are still linear with the network size. In particular, when the network structure is symmetrical about the trap point, the time required for a walker to reach the trap point is the least, that is the transmission efficiency is the highest.