First-passage properties of bundled networks

Bundled networks, obtained by attaching a copy of a fiber structure to each node on the base structure, serve as important realistic models for the geometry and dynamics of nontranslationally invariant systems in condensed matter physics. Here, we analyze the first-passage properties, including the mean first-passage time, the mean-trapping time, the global-mean first-passage time (GFPT), and the stationary distribution, of a biased random walk within such networks, in which a random walker moves to a neighbor on base with probability γ and to a neighbor on fiber with probability 1-γ when the walker at a node on base. We reveal the primary properties of both the base and fiber structure, which govern the first-passage characteristics of the bundled network. Explicit expressions between these quantities in the bundled networks and the related quantities in the component structures are presented. GFPT serves as a crucial indicator for evaluating network transport efficiency. Unexpectedly, bases and fibers with similar scaling of GFPT can construct bundled networks exhibiting different scaling behaviors of GFPT. Therefore, bundled networks can be tailored to accommodate specific dynamic property requirements by choosing a suitable base and fiber structure. These findings contribute to advancing the design and optimization of network structures.