Prematurity disrupts brain development during a critical period of brain growth and organization and is known to be associated with an increased risk of neurodevelopmental impairments. Investigating whole-brain structural connectivity alterations accompanying preterm birth may provide a better comprehension of the neurobiological mechanisms related to the later neurocognitive deficits observed in this population. Using a connectome approach, we aimed to study the impact of prematurity on neonatal whole-brain structural network organization at term-equivalent age. In this cohort study, twenty-four very preterm infants at term-equivalent age (VPT-TEA) and fourteen full-term (FT) newborns underwent a brain MRI exam at term age, comprising T2-weighted imaging and diffusion MRI, used to reconstruct brain connectomes by applying probabilistic constrained spherical deconvolution whole-brain tractography. The topological properties of brain networks were quantified through a graph-theoretical approach. Furthermore, edge-wise connectivity strength was compared between groups. Overall, VPT-TEA infants' brain networks evidenced increased segregation and decreased integration capacity, revealed by an increased clustering coefficient, increased modularity, increased characteristic path length, decreased global efficiency and diminished rich-club coefficient. Furthermore, in comparison to FT, VPT-TEA infants had decreased connectivity strength in various cortico-cortical, cortico-subcortical and intra-subcortical networks, the majority of them being intra-hemispheric fronto-paralimbic and fronto-limbic. Inter-hemispheric connectivity was also decreased in VPT-TEA infants, namely through connections linking to the left precuneus or left dorsal cingulate gyrus - two regions that were found to be hubs in FT but not in VPT-TEA infants. Moreover, posterior regions from Default-Mode-Network (DMN), namely precuneus and posterior cingulate gyrus, had decreased structural connectivity in VPT-TEA group. Our finding that VPT-TEA infants' brain networks displayed increased modularity, weakened rich-club connectivity and diminished global efficiency compared to FT infants suggests a delayed transition from a local architecture, focused on short-range connections, to a more distributed architecture with efficient long-range connections in those infants. The disruption of connectivity in fronto-paralimbic/limbic and posterior DMN regions might underlie the behavioral and social cognition difficulties previously reported in the preterm population.