Connectome embedding in multidimensional graph-invariant spaces

The topological organization of brain networks, or connectomes, can be quantified using graph theory. Here, we investigated brain networks in higher dimensional spaces defined by up to ten node-level graph theoretical invariants. Nodal invariants are intrinsic nodal properties which reflect the topological characteristics of the nodes with respect to the whole network, including segregation (e.g., clustering coefficient) and centrality (e.g., betweenness centrality) measures. Using 100 healthy unrelated subjects from the Human Connectome Project, we generated multiple types of connectomes (structural/functional networks and binary/weighted networks) and embedded the corresponding network nodes (brain regions) into multidimensional graph spaces defined by the invariants. First, we observed that nodal invariants are correlated between them (i.e., they carry similar network information) at a whole-brain and subnetwork level. Second, we conducted a machine learning analysis to test whether brain regions embedded in multidimensional graph spaces can be accurately classified into higher order (association, subcortical and cerebellar) and lower order (visual, somatomotor, attention) areas. Brain regions of higher order and lower order brain circuits were classified with an 80-87% accuracy in a 10-dimensional (10D) space. 10D graph metrics performed better than 2D and 3D graph metrics, and non-linear Gaussian kernels performed better than linear kernels. This suggests a non-linear brain network information gain in a high-dimensional graph space. Finally, we quantified the inter-subject Euclidean distance of each brain region embedded in the multidimensional graph space. The inter-individual distance was largest for regions of the default mode and frontoparietal networks, providing a new avenue for subject-specific network coordinates in a multidimensional space. To conclude, we propose a new framework for quantifying connectome features in multidimensional spaces defined by graph invariants, providing a new avenue for subject-specific network coordinates and inter-individual distance analyses. ### Competing Interest Statement The authors have declared no competing interest.