Volume 86, Number 1, April 2009
|Number of page(s)||6|
|Published online||21 April 2009|
Random walks on the Apollonian network with a single trap
School of Computer Science, Fudan University - Shanghai 200433, China
2 Shanghai Key Lab of Intelligent Information Processing, Fudan University - Shanghai 200433, China
3 Department of Computer Science and Technology, Tongji University - 4800 Cao'an Road, Shanghai 201804, China
Accepted: 16 March 2009
Explicit determination of the mean first-passage time (MFPT) for the trapping problem on complex media is a theoretical challenge. In this paper, we study random walks on the Apollonian network with a trap fixed at a given hub node (i.e., node with the highest degree), which are simultaneously scale-free and small-world. We obtain the precise analytic expression for the MFPT that is confirmed by direct numerical calculations. In the large system size limit, the MFPT approximately grows as a power law function of the number of nodes, with the exponent much less than 1, which is significantly different from the scaling for some regular networks or fractals such as regular lattices, Sierpinski fractals, T-graph, and complete graphs. The Apollonian network is the most efficient configuration for transport by diffusion among all the previously studied structures.
PACS: 05.40.Fb – Random walks and Levy flights / 89.75.Hc – Networks and genealogical trees / 05.60.Cd – Classical transport
© EPLA, 2009
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.