What does 'Linear regularities among words' mean? Context: In the paper "Efficient Estimation of Word Representations in Vector Space" by T. Mikolov et al., the authors make use of the phrase: 'Linear regularities among words'.

What does that mean in the context of the paper, or in a general context related to NLP? 

Quoting the paragraph from the paper:


  Somewhat surprisingly, it was found that similarity of word
  representations goes beyond simple syntactic regularities. Using a
  word offset technique where simple algebraic operations are performed
  on the word vectors, it was shown for example that vector(”King”) -
  vector(”Man”) + vector(”Woman”) results in a vector that is closest to
  the vector representation of the word Queen [20].
  
  In this paper, we try to maximize accuracy of these vector operations
  by developing new model architectures that preserve the linear
  regularities among words. We design a new comprehensive test set for
  measuring both syntactic and semantic regularities1 , and show that
  many such regularities can be learned with high accuracy. Moreover, we
  discuss how training time and accuracy depends on the dimensionality
  of the word vectors and on the amount of the training data.
By linear regularities among words, he meant that "Vectorized form of words should follow linear additive properties!"

V("King") - V("Man") + V("Woman") ~ V("Queen)