Preterm birth is associated with a high prevalence of adverse neurodevelopmental outcome. Non-invasive techniques which can probe the neural correlates underpinning these deficits are required. This can be achieved by measuring the structural network of connections within the preterm infant's brain using diffusion MRI and tractography. We used diffusion MRI and T2 relaxometry to identify connections with altered white matter properties in preterm infants compared to term infants. Diffusion and T2 data were obtained from 9 term neonates and 18 preterm-born infants (born <32 weeks gestational age) at term equivalent age. Probabilistic tractography incorporating multiple fibre orientations was used in combination with the Johns Hopkins neonatal brain atlas to calculate the structural network of connections. Connections of altered diffusivity or T2, as well as their relationship with gestational age at birth and postmenstrual age at the time of MRI, were identified using the network based statistic framework. A total of 433 connections were assessed. FA was significantly reduced in 17, and T2 significantly increased in 18 connections in preterm infants, following correction for multiple comparisons. Cortical networks associated with affected connections mainly involved left frontal and temporal cortical areas: regions which are associated with working memory, verbal comprehension and higher cognitive function--deficits which are often observed later in children and adults born preterm. Gestational age at birth correlated with T2, but not diffusion in several connections. We found no association between diffusion or T2 and postmenstrual age at the time of MRI in preterm infants. This study demonstrates that alterations in the structural network of connections can be identified in preterm infants at term equivalent age, and that incorporation of non-diffusion measures such as T2 in the connectome framework provides complementary information for the assessment of brain development.