### Abstract

Topology of urban environments can be represented by means of graphs. We explore the graph representations of several compact urban patterns by random walks. The expected time of recurrence and the expected first passage time to a node scales apparently linearly in all urban patterns we have studied. In space syntax theory, a positive relation between the local property of a node (qualified by connectivity or by the recurrence time) and the global property of the node (estimated in our approach by the first passage time to it) is known as intelligibility. Our approach, based on random walks, allows us to extend the notion of intelligibility onto the entire domain of complex networks and graph theory.

Original language | English |
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Pages (from-to) | 2153-2167 |

Number of pages | 15 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 464 |

Issue number | 2096 |

DOIs | |

State | Published - Aug 8 2008 |

### Keywords

- First passage times
- Random walks
- Recurrence times
- Space syntax