Intelligibility and First Passage Times In Complex Urban Networks

TL;DR

This paper uses graph theory and random walks to analyze urban network topology, revealing linear scaling of recurrence and passage times, and extends the concept of intelligibility from space syntax to complex networks.

Contribution

It introduces a novel approach using random walks to quantify intelligibility in complex urban networks, linking local and global properties.

Findings

Expected recurrence and first passage times scale linearly in studied urban patterns.

The approach generalizes the concept of intelligibility to complex networks.

Provides a quantitative framework connecting local connectivity with global accessibility.

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 to extend the notion of intelligibility onto the entire domain of complex networks and graph theory.