Christopher Alexander, a British-American scholar, famously differentiated an old (natural) city from a new (planned) one in structure. The former resembles a “semilattice”, or a complex system encompassing many interconnected sub-systems. The latter is shaped in a graph-theoretical “tree”, which lacks the structural complexity as its sub-systems are compartmentalized into a single hierarchy. This structural distinction can explain, or perhaps determine “the patina of life” in old urban districts and the lack of such in new ones. Alexander's idea, although widely influential, remains contested for its lack of empirical support. Subsequent literature failed to distinguish the structural differences between the old and new cities in systematic ways, nor is his asserted structure-life relationship verified with rigor. This study aims to test Alexander’s urban structural theory under a comprehensive research framework. We translated his constructs and premises into a mathematically testable form. The structural qualities of an urban street network, conceived as “semilattice”, “complex network” and “living structure”, were measured using graph-topological indicators. Urban life was captured using a combination of Twitter activities, Point-Of-Interests, and walking trips, aggregated at the district level. The structure-life relationship was tested statistically, after controlling for urban form and socio-demographic confounders, including land use, density, block size, parks, income, age, and demographics. This research design was implemented in London, New York, Hong Kong, and Gdansk. Our results support Alexander's early works that an old urban district contains more “semilattice” than new ones. This quality can be captured by Meshedness Coefficient, a graph-network indicator for a semilattice-shaped street network and a strong predictor for urban life. The same cannot be observed for “complex network” with consistency, and we found no independent associations between “living structure” and life, contrary to existing literature. The study shed light on the hidden relationships between urban spatial structure and behaviors, in both the virtual and physical world. We uncovered the British-American predilection of Alexander’s theory, which is well-supported by observations in London and New York yet less so in Hong Kong or Gdansk, suggesting the need for a locally-sensitive approach. The analytical tools developed can be of value for planning research and practice.