Random walks in unweighted and weighted modular scale-free networks with a perfect trap
arXiv:1311.6956 · doi:10.1063/1.4835655
Abstract
Designing optimal structure favorable to diffusion and effectively controlling the trapping process are crucial in the study of trapping problem---random walks with a single trap. In this paper, we study the trapping problem occurring on unweighted and weighted networks, respectively. The networks under consideration display the striking scale-free, small-world, and modular properties, as observed in diverse real-world systems. For binary networks, we concentrate on three cases of trapping problems with the trap located at a peripheral node, a neighbor of the root with the least connectivity, and a farthest node, respectively. For weighted networks with edge weights controlled by a parameter, we also study three trapping problems, in which the trap is placed separately at the root, a neighbor of the root with the least degree, and a farthest node. For all the trapping problems, we obtain the analytical formulas for the average trapping time (ATT) measuring the efficiency of the trapping process, as well as the leading scaling of ATT. We show that for all the trapping problems in the binary networks with a trap located at different nodes, the dominating scalings of ATT reach the possible minimum scalings, implying that the networks have optimal structure that is advantageous to efficient trapping. Furthermore, we show that for trapping in the weighted networks, the ATT is controlled by the weight parameter, through modifying which, the ATT can behave superlinealy, linearly, sublinearly, or logarithmically with the system size. This work could help improving the design of systems with efficient trapping process and offers new insight into control of trapping in complex systems.
Definitive version accepted for publication in Journal of Chemical Physics
References in corpus (22)
- Modularity and community structure in networks
- Uncovering the overlapping community structure of complex networks in nature and society
- First-passage times in complex scale-invariant media
- Exact Controllability of Complex Networks
- Exact mean first-passage time on the T-graph
- Exact solution for mean first-passage time on a pseudofractal scale-free web
- Occupation times of random walks in confined geometries: From random trap model to diffusion limited reactions
- Survival Probabilities in Coherent Exciton Transfer with Trapping
- Determining mean first-passage time on a class of treelike regular fractals
- Random walks in weighted networks with a perfect trap: An application of Laplacian spectra
- Trapping in complex networks
- Random walks on the Apollonian network with a single trap
- Trapping in dendrimers and regular hyperbranched polymers
- Influence of trap location on the efficiency of trapping in dendrimers and regular hyperbranched polymers
- Average distance in a hierarchical scale-free network: an exact solution
- Mean first-passage time for random walks in general graphs with a deep trap
- Anomalous behavior of trapping on a fractal scale-free network
- Trapping of Continuous-Time Quantum walks on Erdos-Renyi graphs
- Constrained spin dynamics description of random walks on hierarchical scale-free networks
- Controlling the efficiency of trapping in treelike fractals
- Optimal scale-free network with a minimum scaling of transport efficiency for random walks with a perfect trap
- Random Walks on Complex Networks