The Collaborative International Dictionary of English v.0.48:

Knottiness \Knot"ti*ness\, n. [From Knotty.]
   1. The quality or state of being knotty or full of knots.
      [1913 Webster]

   2. Difficulty of solution; intricacy; complication. "
      Knottiness of his style." --Hare.
      [1913 Webster]

WordNet (r) 3.0 (2006):

knottiness
    n 1: puzzling complexity [syn: complicatedness,
         complication, knottiness, tortuousness]