Connectomes' topological organization can be quantified using graph theory. Here, we investigated brain networks in higher dimensional spaces defined by up to ten graph-theoretic nodal properties. These properties assign a score to nodes, reflecting their meaning in the network. Using 100 healthy unrelated subjects from the Human Connectome Project, we generated various connectomes (structural/functional, binary/weighted). We observed that nodal properties are correlated (i.e., they carry similar information) at whole-brain and subnetwork level. We conducted an exploratory machine learning analysis to test whether high dimensional network information differs between sensory and association areas. Brain regions of sensory and association networks were classified with an 80-86% accuracy in a 10D space. We observed the largest gain in machine learning accuracy going from a 2D to 3D space, with a plateauing accuracy towards 10D space, and nonlinear Gaussian kernels outperformed linear kernels. Finally, we quantified the Euclidean distance between nodes in a 10D graph space. The multidimensional Euclidean distance was highest across subjects in the default mode network (in structural networks) and frontoparietal and temporal lobe areas (in functional networks). To conclude, we propose a new framework for quantifying network features in high-dimensional spaces that may reveal new network properties of the brain.

Nodal properties are of particular importance when investigating patterns in brain networks. Nodal information is usually studied by comparing a few nodal measurements (up to 3), resulting in analyses in 3-dimensional spaces, at maximum. We offer a new framework to extend these approaches by defining new, up to 10-dimensional, mathematical spaces, called graph spaces, built using up to 10 nodal properties. We show that correlations between nodal properties express differences regarding connectome models (structural/functional, binary/weighted) and brain subnetworks. We provide early application and quantification of machine learning in graph spaces of dimensions 2 to 10, as well as a quantification of single brain regions, and global connectome, Euclidean distance in a 10-dimensional graph space. This provides new tools to quantify network features in high-dimensional spaces.

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Handling Editor: Olaf Sporns

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