### Abstract

In this paper the following Markov chains are considered: the state space is the set of vertices of a connected graph, and for each vertex the transition is always to an adjacent vertex, such that each of the adjacent vertices has the same probability. Detailed results are given on the expectation of recurrence times, of first-entrance times, and of symmetrized first-entrance times (called commuting times). The problem of characterizing all connected graphs for which the commuting time is constant over all pairs of adjacent vertices is solved almost completely.

Original language | English |
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Pages (from-to) | 311-336 |

Journal | Stochastic processes and their applications |

Volume | 2 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1974 |

### Keywords

- first entrance time
- block of a graph
- tree-wise join
- Random walk
- Balanced graph

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## Cite this

Gobel, F., & Jagers, A. A. (1974). Random walks on graphs.

*Stochastic processes and their applications*,*2*(4), 311-336. https://doi.org/10.1016/0304-4149(74)90001-5