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Conventional connectome edge weights, such as number of streamlines (NOS) or diffusion tensor imaging (DTI) metrics, lack specificity to microstructural details which may hold relevance for macroscale brain organisation. Since biophysical diffusion modelling offers greater specificity to microstructure, we investigated whether parameters from the Standard Model of diffusion in white matter provide informative alternatives for connectome weights – namely the intra-axonal signal fraction (f) and perpendicular extra-axonal diffusivity (D e Perp ), as proxies of axonal density and myelination, respectively. Using diffusion MRI data from healthy adults, we constructed structural networks at four parcellation scales, weighted by f, D e Perp , NOS, fractional anisotropy (FA) and radial diffusivity (RD). While all weights reproduced expected small-world properties, only D e Perp and normalised NOS captured non-random properties of local organisation across all spatial scales. We then correlated each weighted connectome with resting-state fMRI functional connectivity and intracranial measurements of conduction velocity. At the whole-brain level, although NOS gave strongest coupling with fMRI functional connectivity, only D e Perp exhibited significant structure-function coupling across all spatial scales and modalities. At the regional level, D e Perp and RD gave highest consistency in structure-function coupling across spatial scales. Thus, connectome weights derived from D e Perp capture meaningful aspects of brain network organisation with functional relevance.