The Small-World of Human Language

Words in human language interact within sentences in nonrandom ways, and allow humans to construct an astronomic variety of sentences from a limited number of discrete units. This construction process is extremely fast and robust. The co-ocurrence of words within sentences reflect language organization in a subtle manner which can be described in terms of a graph of word interactions. Here we show that such graph displays two important features recently found in a disparate number of complex systems: (a) The so-called small-world effect. In particular, the average distance between two words $d$ (i.e. the average minimum number of jumps to be made from an arbitrary word to another) is shown to be $d \approx 2$ to $3$, in spite that the human brain can store many thousands. (b) A scale-free distribution of degrees. The known dramatic effects of disconnecting the most connected vertices in such networks can be identified in some language disorders. These observations suggest some unexpected features of language organization that might reflect the evolutionary and social history of lexicons and the origins of their flexibility and combinatorial nature.