  It is often stated that human languages, as other biological systems, are
shaped by cost-cutting pressures but, to what extent? Attempts to quantify the
degree of optimality of languages by means of an optimality score have been
scarce and focused mostly on English. Here we recast the problem of the
optimality of the word order of a sentence as an optimization problem on a
spatial network where the vertices are words, arcs indicate syntactic
dependencies and the space is defined by the linear order of the words in the
sentence. We introduce a new score to quantify the cognitive pressure to reduce
the distance between linked words in a sentence. The analysis of sentences from
93 languages representing 19 linguistic families reveals that half of languages
are optimized to a 70% or more. The score indicates that distances are not
significantly reduced in a few languages and confirms two theoretical
predictions, i.e. that longer sentences are more optimized and that distances
are more likely to be longer than expected by chance in short sentences. We
present a new hierarchical ranking of languages by their degree of
optimization. The new score has implications for various fields of language
research (dependency linguistics, typology, historical linguistics, clinical
linguistics and cognitive science). Finally, the principles behind the design
of the score have implications for network science.
