Myelin plays a crucial role in how well information travels between brain regions. Complementing the structural connectome, obtained with diffusion MRI tractography, with a myelin-sensitive measure could result in a more complete model of structural brain connectivity and give better insight into white-matter myeloarchitecture. In this work we weight the connectome by the longitudinal relaxation rate (R1), a measure sensitive to myelin, and then we assess its added value by comparing it with connectomes weighted by the number of streamlines (NOS). Our analysis reveals differences between the two connectomes both in the distribution of their weights and the modular organization. Additionally, the rank-based analysis shows that R1 can be used to separate transmodal regions (responsible for higher-order functions) from unimodal regions (responsible for low-order functions). Overall, the R1-weighted connectome provides a different perspective on structural connectivity taking into account white matter myeloarchitecture.