Developments in non-invasive diffusion MRI tractography techniques have permitted the investigation of both the anatomy of white matter pathways connecting grey matter regions and their structural integrity. In parallel, there has been an expansion in automated techniques aimed at parcellating grey matter into distinct regions based on functional imaging. Here we apply independent component analysis to whole-brain tractography data to automatically extract brain networks based on their associated white matter pathways. This method decomposes the tractography data into components that consist of paired grey matter ‘nodes’ and white matter ‘edges’, and automatically separates major white matter bundles, including known cortico-cortical and cortico-subcortical tracts. We show how this framework can be used to investigate individual variations in brain networks (in terms of both nodes and edges) as well as their associations with individual differences in behaviour and anatomy. Finally, we investigate correspondences between tractography-based brain components and several canonical resting-state networks derived from functional MRI.