During the 3rd trimester, large-scale neural circuits are formed in the human brain, resulting in a highly efficient and segregated connectome at birth. Despite recent findings identifying important preterm human brain network properties such as rich-club organization, how the structural network develops differentially across brain regions and among different types of connections in this period is not yet known. Here, using high resolution diffusion MRI of 77 preterm-born and full-term neonates scanned at 31.9-41.7 postmenstrual weeks (PMW), we constructed structural connectivity matrices and performed graph-theory-based analyses. Faster increases of nodal efficiency were mainly located at the brain hubs distributed in primary sensorimotor regions, superior-middle frontal, and precuneus regions during 31.9-41.7PMW. Higher rates of edge strength increases were found in the rich-club and within-module connections, compared to other connections. The edge strength of short-range connections increased faster than that of long-range connections. Nodal efficiencies of the hubs predicted individual postmenstrual ages more accurately than those of non-hubs. Collectively, these findings revealed more rapid efficiency increases of the hub and rich-club connections as well as higher developmental rates of edge strength in short-range and within-module connections. These jointly underlie network segregation and differentiated emergence of brain functions.