The functional organization of the brain is usually presented with a back-to-front gradient of timescales, reflecting regional specialization with sensory areas (back) processing information faster than associative areas (front), which perform information integration. However, cognitive processes require not only local information processing but also coordinated activity across regions. Using magnetoencephalography recordings, we find that the functional connectivity at the edge level (between two regions) is also characterized by a back-to-front gradient of timescales following that of the regional gradient. Unexpectedly, we demonstrate a reverse front-to-back gradient when nonlocal interactions are prominent. Thus, the timescales are dynamic and can switch between back-to-front and front-to-back patterns.