What is "treeness"

n. 1 (context nonce English) The essence of what it means to be a tree; the quality that make a tree what it is. 2 (context genetics English) 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 evolve independently after they split. 3 (context graph theory English) The condition of being a tree; acyclicity and connectedness.