TY - JOUR

T1 - Return times of random walk on generalized random graphs

AU - Masuda, Naoki

AU - Konno, Norio

N1 - Funding Information:
We thank H. Kesten and G. F. Lawler for helpful comments. This study is supported by a Grant-in-Aid for Scientific Research (JSPS) and a Grant-in-Aid for Scientific Research (B) (Grant No. 12440024) of the Japan Society of the Promotion of Science.

PY - 2004/6

Y1 - 2004/6

N2 - The analytic expressions for the probability distributions of first and general return times were derived for generalized random networks. The method was useful in saving the computation time and hence obtaining return time probabilities on a much longer time scale than with simulations. It was found that the scale-free networks and ER random graphs yield slower decay of return time probabilities than the Cayley trees with the corresponding vertex degrees. The asymptotic behavior of random walk suggests that global orders are consequences in networks with heterogeneous vertex degrees such as ER random and scale-free networks.

AB - The analytic expressions for the probability distributions of first and general return times were derived for generalized random networks. The method was useful in saving the computation time and hence obtaining return time probabilities on a much longer time scale than with simulations. It was found that the scale-free networks and ER random graphs yield slower decay of return time probabilities than the Cayley trees with the corresponding vertex degrees. The asymptotic behavior of random walk suggests that global orders are consequences in networks with heterogeneous vertex degrees such as ER random and scale-free networks.

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U2 - 10.1103/PhysRevE.69.066113

DO - 10.1103/PhysRevE.69.066113

M3 - Article

C2 - 15244673

AN - SCOPUS:42749108755

SN - 1063-651X

VL - 69

SP - 066113-1-066113-7

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 6 2

M1 - 066113

ER -