Stability of strength and weight distributions for time-evolving word Co-occurrence networks

© 2014 Springer International Publishing Switzerland. The most intriguing and celebrated empirical law in quantitative linguistics is Zipf's law [6], which in one of its forms states that the distribution of word frequencies in a text follows a power law with exponent γ ∼ 2. At least in a qualitative sense, the fulfillment of Zipf's law is astonishing, being valid no matter the author, style, or language [4-6]. An important problem of Zipf's law is the variation of the exponent γ among different samples. Although the dependence of γ with system size was firstly acknowledged by Zipf himself [6], and later on other authors have confirmed it [1, 2], few systematic studies on these dependence have been performed. This can be formulated within the framework of (directed) networks, where words (types) are nodes, and consecutive appearances of word tokens increase the weight wij of a link between the two nodes by an amount equal to one. In this way, the frequency of a word is equivalent to the strength si = j wij of its corresponding node.