MRI connectomics methods treat the brain as a network and provide new information about its organization, efficiency, and mechanisms of disruption. The most commonly used method of defining network nodes is to register the brain to a standardized anatomical atlas based on the Brodmann areas. This approach is limited by inter-subject variability and can be especially problematic in the context of brain maturation or neuroplasticity (cerebral reorganization after brain damage). In this study, we combined different image processing and network theory methods and created a novel approach that enables atlas-free construction and connection-wise comparison of diffusion MRI-based brain networks. We illustrated the proposed approach in three age groups: neonates, 6-month-old infants, and adults. First, we explored a data-driven method of determining the optimal number of equal-area nodes based on the assumption that all cortical areas of the brain are connected and, thus, no part of the brain is structurally isolated. Second, to enable a connection-wise comparison, alignment to a "reference brain" was performed in the network domain within each group using a matrix alignment algorithm with simulated annealing. The correlation coefficients after pair-wise network alignment ranged from 0.6102 to 0.6673. To test the method's reproducibility, one subject from the 6-month-old group and one from the adult group were scanned twice, resulting in correlation coefficients of 0.7443 and 0.7037, respectively. While being less than 1 due to parcellation and noise, statistically, these values were significantly higher than inter-subject values. Rotation of the parcellation largely explained the variability. Through the abstraction from anatomy, the developed framework allows for a fully network-driven analysis of structural MRI connectomes and can be applied to subjects at any stage of development and with substantial differences in cortical anatomy.