The quality or degree of having branches; the state of being branched or subdivided.
From branched (adjective) + -ness (abstract noun suffix), creating a noun that describes the property or extent of branching in a structure.
Scientists measure branchedness in nerve cells and blood vessels because more branchedness usually means better distribution and faster communication, which is why your brain gets increasingly 'bushy' as you learn.
Complete word intelligence in one call. Free tier — 50 lookups/day.