treeness

noun3

1. •
   The essence of what it means to be a tree; the qualities that make a tree what it is.

   • A word represents the entity but not THE entity itself. "tree" is not a tree, you can call it "ca^y" or whatever but the conceptual meaning of treeness stays the same. — 1999
2. •
   The suitability of an evolutionary tree for representing the structure of a population; the degree to which a population structure can be accurately described as a tree of descent, with different branches evolving independently after they split.

   • Failing to statistically test for treeness, they reify the evolutionary trajectories assumed at the outset. — 2007
3. •
   The condition of being a tree; acyclicity and connectedness.

   • …such a tree can be built up incrementally by adding the shortest edge not yet explored, which also maintains treeness (acyclicity). — 1998