Words in human language interact in sentences in non–random 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–occurrence of words in sentences reflects language organization in a subtle manner that can be described in terms of a graph of word interactions. Here, we show that such graphs display two important features recently found in a disparate number of complex systems. (i) The so called small–world effect. In particular, the average distance between two words, d (i.e. the average minimum number of links to be crossed from an arbitrary word to another), is shown to be d≈ 2–3, even though the human brain can store many thousands. (ii) A scale–free distribution of degrees. The known pronounced effects of disconnecting the most connected vertices in such networks can be identified in some language disorders. These observations indicate 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.

The emergence of a complex language is one of the fundamental events of human evolution, and several remarkable features suggest the presence of fundamental principles of organization. These principles seem to be common to all languages. The best known is the so-called Zipf's law, which states that the frequency of a word decays as a (universal) power law of its rank. The possible origins of this law have been controversial, and its meaningfulness is still an open question. In this article, the early hypothesis of Zipf of a principle of least effort for explaining the law is shown to be sound. Simultaneous minimization in the effort of both hearer and speaker is formalized with a simple optimization process operating on a binary matrix of signal–object associations. Zipf's law is found in the transition between referentially useless systems and indexical reference systems. Our finding strongly suggests that Zipf's law is a hallmark of symbolic reference and not a meaningless feature. The implications for the evolution of language are discussed. We explain how language evolution can take advantage of a communicative phase transition.

Networks of interconnected nodes have long played a key role in Cognitive Science, from artificial neural networks to spreading activation models of semantic memory. Recently, however, a new Network Science has been developed, providing insights into the emergence of global, system-scale properties in contexts as diverse as the Internet, metabolic reactions, and collaborations among scientists. Today, the inclusion of network theory into Cognitive Sciences, and the expansion of complex-systems science, promises to significantly change the way in which the organization and dynamics of cognitive and behavioral processes are understood. In this paper, we review recent contributions of network theory at different levels and domains within the Cognitive Sciences.

Many languages are spoken on Earth. Despite their diversity, many robust language universals are known to exist. All languages share syntax, i.e., the ability of combining words for forming sentences. The origin of such traits is an issue of open debate. By using recent developments from the statistical physics of complex networks, we show that different syntactic dependency networks (from Czech, German, and Romanian) share many nontrivial statistical patterns such as the small world phenomenon, scaling in the distribution of degrees, and disassortative mixing. Such previously unreported features of syntax organization are not a trivial consequence of the structure of sentences, but an emergent trait at the global scale.