The distribution of first hitting times of randomwalks on Erdős–Rényi networks

@article{Tishby2017TheDO,
  title={The distribution of first hitting times of randomwalks on Erdős–R{\'e}nyi networks},
  author={Ido Tishby and Ofer Biham and Eytan Katzav},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2017},
  volume={50}
}
Analytical results for the distribution of first hitting times of random walks on Erdős–Rényi networks are presented. Starting from a random initial node, a random walker hops between adjacent nodes until it hits a node which it has already visited before. At this point, the path terminates. The path length, namely the number of steps, d, pursued by the random walker from the initial node up to its termination is called the first hitting time or the first intersection length. Using recursion… 

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References

SHOWING 1-10 OF 59 REFERENCES

The distribution of path lengths of self avoiding walks on Erdős–Rényi networks

An analytical and numerical study of the paths of self avoiding walks (SAWs) on random networks shows that the pruned networks maintain a Poisson degree distribution, with an average degree, 〈 k 〉 t , that decreases linearly in time.

Analytical results for the distribution of shortest path lengths in random networks

We present two complementary analytical approaches for calculating the distribution of shortest path lengths in Erdős-Rényi networks, based on recursion equations for the shells around a reference

First-passage properties of the Erdos Renyi random graph

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.

Self-avoiding walks on scale-free networks.

  • C. Herrero
  • Mathematics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2005
Long-range properties of random SAW's on scale-free networks, characterized by a degree distribution P(k) approximately k(-gamma), and the dependence of alpha on the minimum allowed degree in the network are discussed.

A model of self‐avoiding random walks for searching complex networks

An analytical model is proposed to estimate the average search length of a SAW when used to locate a resource in a network, which is a mean‐field model, whose applicability to real networks is validated by simulation.

Kinetic growth walks on complex networks

Kinetically grown self-avoiding walks on various types of generalized random networks have been studied. Networks with short- and long-tailed degree distributions P(k) were considered (k, degree or

Self-avoiding walks and connective constants in small-world networks.

This work considers networks generated by rewiring links in one- and two-dimensional regular lattices by means of self-avoiding walks and derives results agreeing with each other for small p and differ for p close to 1, because of the different connectivity distributions resulting in both cases.

Random Walks on Lattices. II

Formulas are obtained for the mean first passage times (as well as their dispersion) in random walks from the origin to an arbitrary lattice point on a periodic space lattice with periodic boundary

The average number of distinct sites visited by a random walker on random graphs

An expression for the graph topology-dependent prefactor B in S(n) = Bn is proposed and generating function techniques are used to relate this prefactor to the graph adjacency matrix and then devise message-passing equations to calculate its value.

Exploring complex networks through random walks.

  • L. D. CostaG. Travieso
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2007
This article considers random, Barabási-Albert (BA), and geographical network models with varying connectivity explored by three types of random walks: traditional, preferential to untracked edges, and preferential to unvisited nodes to derive results on node and edge coverage efficiency.
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