High-entropy alloys (HEAs) exhibit exceptionally good combinations of properties recently reported to correlate with chemical short-range ordering (cSRO). However, in atomistic simulations, their state of cSRO has only been so far characterized using the Warren-Cowley parameters. Yet, this approach is incomplete as distinct local atomic configurations sharing the same chemical concentration are indistinguishable. Here, we propose a generalized framework, based on graph-convolution neural networks equivariant to E(3) symmetry operations, statistical mechanics, and information theory, capable of completely identifying the set of distinct local atomic bonding environments and their associated population densities in HEAs. This approach leads to a quantitative characterization of the cSRO state and provides a predictive framework for evaluation of cSRO domain sizes, thus offering novel avenues to explore the relationships between processing, structure, and properties in HEAs.