Adjusting the Trapping Process of a Directed Weighted Edge-Iteration Network

Controlling the trapping process is one of the important themes in the study of random walk in real complex systems. We studied two types of random walks that are different from the traditional random walk on a directed weighted network. The first type of random walk is the weighted random walk controlled by the weight θ, and the other is the delayed-weighted random walk affected by both delay probability p and weight θ. Furthermore, we derived analytically the average trapping time (ATT) measuring the efficiency of the two types of trapping processes; the result shows that the ATT grows sub-linearly, linearly, and super-linearly with the network order when the weight satisfies θ32 , respectively. The weight θ of the directed network can be adjusted by direction, the delay parameter p only changes the pre-factor of the ATT, and the weight θ modifies both the pre-factor and scaling of the ATT.