treeness

Noun

treeness (uncountable)

1. (nonce-word) The essence of what it means to be a tree; the qualities that make a tree what it is.
   • A tree may, for the imagination, present forcibly one of its qualities at a time; it may be a green dome of shade on a hot day, a ladder of retreat for a man from the attentions of a mad bull, a peg on which an apple hangs, a screen for an assassin, a choir for birds; and its own business of...1912, D. S. MacColl, "A Year of 'Post-Impressionism'", in The Living Age, volume CCLXXIII, The Living Age Company, page 163
   • 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 April 18, Sans Will, “Re: DCC and Logic add a bit of philosophy and voila!..”, in soc.culture.vietnamese (Usenet)
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.
   • If factors that contribute to a tree-like pattern of the variance–covariance matrix dominate the evolutionary picture over those that tend to destroy it, one can expect treeness to be reasonably high. Only if this is true, reconstruction of the evolutionary process by tree analysis and a tree...1974, L. L. Cavalli-Sforza, A. Piazza, “Analysis of Evolution: Evolutionary Rates, Independence and Treeness”, in Theoretical Population Biology, volume 8, page 159
   • The computer programs used to generate “trees” from genetic distance data will do so regardless of what evolutionary factors generated the distances. It is therefore the obligation of the users of such programs to ensure that the genetic distance data have the properties of treeness before...1999, Alan R. Templeton, “Human Races: A Genetic and Evolutionary Perspective”, in American Anthropologist, volume 100, pages 638–639
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, Joseph O'Rourke, Computational Geometry in C, 2nd edition, Cambridge University Press, →ISBN, page 174
   • …every link that gives rise to a cycle into the graph (viz., that destroys the graph’s “treeness”) is eliminated….2010, Massimo Buscema, Pier L. Sacco, “Auto-contractive Maps, the H Function, and the Maximally Regular Graph (MRG)”, in Vittorio Capecchi et al., editors, Applications of Mathematics in Models...