Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2007-09-18
Phys. Rev. E 77, 061113 (2008)
Physics
Condensed Matter
Disordered Systems and Neural Networks
12 pages, 8 figures; added new results and discussion; added appendix on numerical procedures. To appear in PRE
Scientific paper
10.1103/PhysRevE.77.061113
An analytic effective medium theory is constructed to study the mean access times for random walks on hybrid disordered structures formed by embedding complex networks into regular lattices, considering transition rates $F$ that are different for steps across lattice bonds from the rates $f$ across network shortcuts. The theory is developed for structures with arbitrary shortcut distributions and applied to a class of partially-disordered traversal enhanced networks in which shortcuts of fixed length are distributed randomly with finite probability. Numerical simulations are found to be in excellent agreement with predictions of the effective medium theory on all aspects addressed by the latter. Access times for random walks on these partially disordered structures are compared to those on small-world networks, which on average appear to provide the most effective means of decreasing access times uniformly across the network.
Candia Julián
Kenkre V. M.
Parris Paul E.
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