Optimal scale-free network with a minimum scaling of transport efficiency for random walks with a perfect trap

Abstract

Average trapping time (ATT) is central in the trapping problem since it is a key indicator characterizing the efficiency of the problem. Previous research has provided the scaling of a lower bound of the ATT for random walks in general networks with a deep trap. However, it is still not well understood in which networks this minimal scaling can be reached. Particularly, explicit quantitative results for ATT in such networks, even in a specific network, are lacking, in spite that such networks shed light on the design for optimal networks with the highest trapping efficiency. In this paper, we study the trapping problem taking place on a hierarchical scale-free network with a perfect trap. We focus on four representative cases with the immobile trap located at the root, a peripheral node, a neighbor of the root with a single connectivity, and a farthest node from the root, respectively. For all the four cases, we obtain the closed-form formulas for the ATT, as well as its leading scalings. We show that for all the four cases of trapping problems, the dominating scalings of ATT can reach the predicted minimum scalings. This work deepens the understanding of behavior of trapping in scale-free networks, and is helpful for designing networks with the most efficient transport process.

Definitive version accepted for publication in The Journal of Chemical Physics

References in corpus (28)

• Emergence of scaling in random networks
• Hierarchical organization of modularity in metabolic networks
• First-passage times in complex scale-invariant media
• Deterministic Scale-Free Networks
• Random walks on graphs: ideas, techniques and results
• Global mean first-passage times of random walks on complex networks
• First passage time for random walks in heterogeneous networks
• Exact mean first-passage time on the T-graph
• Exact solution for mean first-passage time on a pseudofractal scale-free web
• Coherent exciton transport in dendrimers and continuous-time quantum walks
• Random Walks on deterministic Scale-Free networks: Exact results
• Exact calculations of first-passage quantities on recursive networks
• Determining mean first-passage time on a class of treelike regular fractals
• Exact scaling properties of a hierarchical network model
• Trapping in complex networks
• Trapping in dendrimers and regular hyperbranched polymers
• Effective target arrangement in a deterministic scale-free graph
• Trapping in scale-free networks with hierarchical organization of modularity
• Distinct scalings for mean first-passage time of random walks on scale-free networks with the same degree sequence
• Close or connected? Distance and connectivity effects on transport in networks
• Exactly solvable scale-free network model
• Random walks in modular scale-free networks with multiple traps
• Average distance in a hierarchical scale-free network: an exact solution
• Trapping time statistics and efficiency of transport of optical excitations in dendrimers
• Role of fractal dimension in random walks on scale-free networks
• Mean first-passage time for random walks in general graphs with a deep trap
• Trapping of Continuous-Time Quantum walks on Erdos-Renyi graphs
• Complete spectrum of stochastic master equation for random walks on treelike fractals

Cited by in corpus (5)

• Influence of trap location on the efficiency of trapping in dendrimers and regular hyperbranched polymers
• Controlling the efficiency of trapping in treelike fractals
• Maximal entropy random walk improves efficiency of trapping in dendrimers
• Random walks in unweighted and weighted modular scale-free networks with a perfect trap
• Anomalous behavior of trapping in extended dendrimers with a perfect trap