Scaling of average receiving time on double-weighted polygon networks

Abstract

In this paper, we introduce a class of double-weighted polygon networks with two different meanings of weighted factors [Formula: see text] and [Formula: see text], which represent path-difficulty and path-length, respectively, based on actual traffic networks. Picking an arbitrary node from the hub nodes set as the trap node, and the double-weighted polygon networks are divided into [Formula: see text] blocks by combining with the iterative method. According to biased random walks, the calculation expression of average receiving time (ART) of any polygon networks is given by using the intermediate quantity the mean first-passage time (MFPT), which is applicable to any [Formula: see text] ([Formula: see text]) polygon networks. What is more, we display the specific calculation process and results of ART of the double-weighted quadrilateral networks, indicating that ART grows exponentially with respect to the networks order and the exponent is [Formula: see text] which grows with the product of [Formula: see text]. When [Formula: see text] increases, ART increases linearly ([Formula: see text]) or sublinearly ([Formula: see text]) with the size of networks, and the smaller value of [Formula: see text], the higher transportation efficiency.