From one-way streets to percolation on random mixed graphs

Area of Science:

• Network Science
• Statistical Physics
• Urban Planning

Background:

• Street networks are typically modeled as undirected graphs, ignoring the impact of one-way streets on shortest paths.
• The influence of one-way streets on urban traffic flow and network connectivity remains under-explored.

Purpose of the Study:

• To empirically analyze the effect of one-way streets on shortest paths in real-world urban networks.
• To develop and investigate a mixed graph model simulating street networks with one-way streets.
• To understand the phase transition and critical exponents related to network connectivity in the presence of directed links.

Main Methods:

• Empirical analysis of street networks in approximately 140 cities worldwide.
• Development of a 2D regular lattice model with a variable fraction of directed links to mimic one-way streets.
• Numerical computation of the strongly connected component (SCC) size and critical exponents.

Main Results:

• One-way streets introduce detours with a nonuniversal exponent and have a dual effect on traffic patterns (mitigation and bottlenecks).
• A critical threshold (p_c) for directed links was identified, above which the SCC size becomes zero.
• The observed phase transition belongs to a new universality class, distinct from directed and standard percolation.

Conclusions:

• One-way streets significantly alter urban network topology and shortest path characteristics.
• The mixed graph model effectively captures the impact of one-way streets and reveals connections to percolation theory.
• Real-world network transitions can be understood through random perturbations of regular lattices, highlighting the relevance of statistical physics models.