Did Rome's trade network topology reveal imperial collapse before it happened?

Researchers mapped the Roman Empire's trade network as a weighted graph and tracked how its topology changed across four centuries using persistent homology—a technique that counts cycles and loops in a system. They found three distinct phases: stable high-redundancy trade until 200 CE, temporary stress during the third-century crisis (which recovered), and irreversible structural decline from 290 onwards. This topological signature persisted even after imperial reunification, suggesting the network's resilience had fundamentally degraded.