Exact Calculations of First-Passage Quantities on a Class of Weighted Tree-Like Fractal Networks

Abstract

This paper concerns the weight-dependent random walk on a class of weighted tree-like fractal networks controlled by a positive integer parameter [Formula: see text] [Formula: see text] and the weight factor [Formula: see text] [Formula: see text]. We study the first return time (FRT) of a given hub and the global first-passage time (GFPT) to a given hub on the networks. By the probability generating function method, we derive the analytic expressions of the first and second moments of FRT and GFPT. In order to evaluate the fluctuation of FRT and GFPT, we further calculate the variance and the reduced moments of FRT and GFPT.