Connectome studies have been able to demonstrate that the topological organization of the brain is a small world network¹; however, these studies assume that all brain connections are equivalent (i.e. binary connections). Brain networks are also organized in a heterogeneous range of white matter tract sizes, which suggests a broad range of connection strengths. Therefore, the assumption that all connections are equivalent yields an inaccurate picture brain networks. The heterogeneity of connection strengths can be represented in graph theory by applying edge weights to the network². In connectomics, weights have been used as a thresholding method to remove spurious connections and reduce the binary graph density. However, these thresholds are arbitrarily selected, which hinders the ability to compare networks created at different thresholds³. To overcome this limitation and effectively study weighted connectomes, we developed a generalized framework to estimate the topological properties of weighted brain networks. The weighted network is comprised of both strong and weak connections, which offer a more realistic model of the brain. Also the extra degree of freedom that comes with weighting a network provides a more robust model of the brain, which is less dependent on thresholds.The University of Florida Institutional Review Board approved this study. One healthy subject was scanned ten times over the course of one month, which provided ten controlled brain data set from which to determine the network properties across different MRI acquisitions. The subject was scanned in a 3 T Siemens Verio system in the Shands Hospital of the University of Florida. High angular resolution diffusion imaging (HARDI) data was obtained with a spin echo preparation and an echo planar imaging readout using the following parameters: TR/TE = 17300/81 ms, 2 scans without diffusion weighting, 6 diffusion gradient directions with b-value of 100 s/mm² and 64 diffusion gradient directions with b-value of 1000 s/mm². Sixty eight cortical anatomical nodes were segmented ^4,5 using a structural T1-weighted image with an automatic segmentation algorithm in FreeSurfer (Laboratory for Computational Neuroimaging, A. A. Martinos Center for Biomedical Imaging, Charlestown, MA). The structural image and diffusion weighted images was spatially registered using FSL’s FLIRT ⁶ algorithm, using an affine transformation. Employing FLIRT’s transformation matrix output, the FreeSurfer derived nodes were then registered to DWI using FSL’s ApplyXFM. The network edges (Figure 1) are defined by streamlines connecting any two nodes and the edge weight is defined as in Colon-Perez et.al.² We compared the binary framework⁷ and the proposed weighted framework on networks generated at different thresholds. The framework was first tested without applying any threshold, i.e. any two nodes connected by at least one streamline will have an edge. Subsequent networks were generated with thresholds for edges of 25, 50 and 125 or more streamlines.As expected, the binary network density decreased with increasing threshold (Figure 1) from ~50% without any applied threshold, to ~32% for networks made up of edges of 125 streamlines or more, and the binary network degree varied significantly with different thresholds ranging from 12% to 62%. In contrast, the average connection strength of the weighted network for all nodes over all networks was constant across all thresholds; the percentage change for individual nodes ranged from 0% to 0.24%. As expected, the binary network had difficulty determining the small world property for dense networks. The network generated with edges made up with 125 streamlines or more displayed a small world index > 1 indicating that this binary network displayed the small world property. However, the weighted approach also displayed small world indices > 1 but for all thresholds indicating a small world network at all densities. This is the first time a densely-weighted brain network has shown the small world property.The topological network organization of the brain white matter network was derived from diffusion-weighted imaging and deterministic tractography using a network model with weighted edges. The weighted brain networks model more accurately reflects the actual structure of the brain and has the advantage of reducing the need for thresholding to obtain topological properties in dense and weighted connectomes (Figure 2). As threshold changes, the variability in measures of connectivity (i.e. degree vs node strength) across the ten networks was less in weighted networks than in binary networks. Also the proposed generalized weighted framework was able to demonstrate the small world property of brain networks in high-density graphs in situations where the binary framework did not demonstrate the small world property.