  Brain function and connectivity is a pressing mystery in medicine related to
many diseases. Neural connectomes have been studied as graphs with graph theory
methods including topological methods. Work has started on hypergraph models
and methods where the geometry and topology is significantly different. We
define a hypergraph called the hyper-connectome with joint information entropy
and total correlation. We give the pseudocode for computation from finite
samples. We give the theoretic importance of this generalization's topology and
geometry with respect to random variables and then prove the hypergraph can be
necessary for prediction and classification. We confirm with a simulation study
and computation. We prove the approximation for continuous random variables
with finite samples. We compare connectome versus hyper-connectome for
predicting schizophrenia in subjects based on a fMRI dataset using a linear
support vector machine. The hyper-connectome achieves better performance in
accuracy (up to 56\%) and F1 score (up to 0.52) than the connectome. We reject
null hypothesis at 95\% with p-value = 0.00074.
