Random walks on the Apollonian network with a single trap

Details Random walks on the Apollonian network with a single trap Random walks on the Apollonian network with a single trap

2009-03-17

arxiv.org/abs/0903.2887v1

Europhysics Letters 86 (2009) 10006

Physics

Condensed Matter

Statistical Mechanics

Definitive version accepted for publication in EPL (Europhysics Letters)

Scientific paper

10.1209/0295-5075/86/10006

Explicit determination of the mean first-passage time (MFPT) for 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 previously studied structure.

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