Connectome embedding in multidimensional graph spaces

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 three), resulting in analyses in three-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.