The universality in urban commuting across and within cities

Commuting is a key mechanism that governs the dynamics of cities. Despite its importance, very little is known of the properties and mechanisms underlying this crucial urban process. Here, we capitalize on $\sim$ 50 million individuals' smartphone data from 234 Chinese cities to show that urban commuting obeys remarkable regularities. These regularities can be generalized as two laws: (i) the scale-invariance of the average commuting distance across cities, which is a long-awaited validation of Marchetti's constant conjecture, and (ii) a universal inverted U-shape of the commuting distance as a function of the distance from the city centre within cities, indicating that the city centre's attraction is bounded. Motivated by such empirical findings, we develop a simple urban growth model that connects individual-level mobility choices with macroscopic urban spatial structure and faithfully explains both commuting laws. Our results further show that the scale-invariants of human mobility will ultimately lead to the polycentric transition in cities, which could be used to better inform urban development strategies.