# Return times of random walk on generalized random graphs.

@article{Masuda2004ReturnTO, title={Return times of random walk on generalized random graphs.}, author={Naoki Masuda and Norio Konno}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2004}, volume={69 6 Pt 2}, pages={ 066113 } }

Random walks are used for modeling various dynamics in, for example, physical, biological, and social contexts. Furthermore, their characteristics provide us with useful information on the phase transition and critical phenomena of even broader classes of related stochastic models. Abundant results are obtained for random walk on simple graphs such as the regular lattices and the Cayley trees. However, random walks and related processes on more complex networks, which are often more relevant in…

## 39 Citations

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- Computer Science, MathematicsArXiv
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### Analytical results for the distribution of cover times of random walks on random regular graphs

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We present analytical results for the distribution of cover times of random walks (RWs) on random regular graphs consisting of N nodes of degree c (c ⩾ 3). Starting from a random initial node at time…

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An effective medium approximation is developed that predicts that the mean first-passage time between pairs of nodes, as well as all moments of this first- passage time, are insensitive to the fraction p of occupied links.

### Analytical results for the distribution of first-passage times of random walks on random regular graphs

- Computer Science
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Analytical results for the distribution of FP times of random walks (RWs) on random regular graphs that consist of N nodes of degree c ≥ 3 are found to be in very good agreement with the results obtained from computer simulations.

### Analytical results for the distribution of first return times of random walks on random regular graphs

- Mathematics, Computer ScienceJournal of Physics A: Mathematical and Theoretical
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Analytical results for the distribution of first return (FR) times of random walks (RWs) on random regular graphs (RRGs) consisting of N nodes of degree c ⩾ 3 are presented and are found to be in excellent agreement with the results obtained from computer simulations.

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By numerical simulations, it is shown that the network heterogeneity has a influence on the effect of walk preference in the cascading failure phenomenon and an appropriate degree correlation can guarantee a low risk of cascading failures.

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A method of calculating the variance of FRT on general finite networks is presented and the results differ from those in such other networks as Sierpinski gaskets, Vicsek fractals, T-graphs, pseudofractal scale-free webs, (u, v) flowers, and fractal and non-fractal Scale-free trees.

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Considering the FH event as a termination mechanism of the RW trajectories, these results provide useful insight into the general problem of survival analysis and the statistics of mortality rates when two or more termination scenarios coexist.

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