The average trapping time on the weighted pseudofractal scale-free web

Abstract

Abstract In this paper, we consider the average trapping time (ATT) on the weighted pseudofractal scale-free web (WPSFW) with weight factor r . According to the iteration mechanism of WPSFW, we consider the weight-dependent walk from the node of web subunit to the trap fixed in a hub node. Using the tool of probability generating function, the relationship between the mean first passage time (MFPT) of two generations of the web is discovered, and the expression of the MFPT is obtained. Moreover, we consider the MFPT averaged over all the starting nodes of subunit and finally get the analytical expression of ATT. The result shows that the ATT growth approximates a power-law function of the number of web nodes, and its exponent is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mfrac> <mml:mrow> <mml:mi>ln</mml:mi> <mml:mfrac> <mml:mrow> <mml:mn>4</mml:mn> <mml:mi>r</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>+</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfrac> </mml:mrow> <mml:mrow> <mml:mi>ln</mml:mi> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfrac> </mml:math> .