Optimizing the Trapping (Transport) Efficiency in Regular Branched Networks

Trapping processes are a kind of random walks which have wide range of applications. Controlling and optimizing the trapping (transport) efficiency has been a hot topic in the past several years. In this work, we study how to improve the trapping (transport) efficiency in regular branched networks, also known as Cayley trees, by analyzing biased random walks on a family of weighted Cayley trees whose edges weights are dominated by a parameter r (r>0). Firstly, a method to calculate the quantities for measuring the trapping efficiency on general weighted networks is presented. Then the trapping efficiencies in regular branched networks are evaluated analytically and optimized with respect to parameter r. Three different scenarios, with respect to the location distribution of the trap, are considered, and optimal parameter r, where highest trapping efficiency can be achieved, are obtained.