Optimization of transport efficiency on bundled networks

Bundled networks are important models for representing polymers and noncrystalline solids with branching structures. In this study, we consider unbiased random walks on a bundled network, which is constructed by attaching a copy of a fiber structure to each node of a base graph. We analyze the first-passage properties of this network, including the mean first-passage time, the mean trapping time, and the global-mean first-passage time (GFPT), which serve as a key measure of transport efficiency. Our findings indicate that these quantities are primarily determined by the first-passage properties on both the base and fiber. Exact formulas are derived to describe the relations between these quantities. Furthermore, we propose a general method to control the transport efficiency of bundled networks by introducing a parameter γ. Results show that for different values of γ, the GFPT of the bundled network exhibits distinct scaling behaviors. Therefore, bundled networks with specified transport efficiency can be obtained by carefully choosing the base graph, fiber structure, and parameter γ. These findings provide valuable insights into network design and optimization.