Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2006-08-29
J. Stat. Phys. 129, 323 (2007)
Physics
Condensed Matter
Disordered Systems and Neural Networks
8 pages, 6 figures; expanded discussions, added figures and references. To appear in J Stat Phys
Scientific paper
10.1007/s10955-007-9362-5
We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds ($F$) and across network shortcuts ($f$). For fast shortcuts ($f/F\gg 1 $) and low shortcut densities, traversal time data collapse onto an universal curve, while a crossover behavior that can be related to the percolation threshold of the scale-free network component is identified at higher shortcut densities, in analogy to similar observations reported recently in Newman-Watts small-world networks. Furthermore, we observe that random walk traversal times are larger for networks with a higher degree of inhomogeneity in their shortcut distribution, and we discuss access time distributions as functions of the initial and final node degrees. These findings are relevant, in particular, when considering the optimization of existing information networks by the addition of a small number of fast shortcut connections.
Candia Julián
Kenkre V. M.
Parris Paul E.
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