Barcelona effect: studying the instability of shortest paths in urban settings

Human mobility is one of the important factors affecting the efficiency of cities and the quality of life of their dwellers. However, while city planners aim to improve the urban road network design to satisfy the local mobility demand and distribute traffic in an optimal way, the structure of cities across different areas and countries vary considerably and in complex ways, sometimes being the result of historical stratifications. One question that emerges, then, is how we can characterize cities in terms of (potential) traffic efficiency. In this work we aim to study the problem from a new perspective, introducing the concept of (shortest) path instability, which quantifies the tendency of a road network to provide very different travel alternatives for just slightly different trips. A notable case of that, which stimulated this research, is the city of Barcelona, where, apparently, reaching very close destinations might require very different routes. The concept is implemented and applied to two case studies at different spatial scales, one comparing the European capitals and the other comparing municipalities of an Italian region. Results show that path instability is heterogeneously distributed, with some largely unstable cities and others very stable, and it is not directly determined by simple city characteristics, such as the city size or its "smartness".