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Word-Length Correlations and Memory in Large Texts: A Visibility Network Analysis

Unidad Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, Av. IPN No. 2580, L. Ticomán, México D.F., 07340, Mexico
Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, México D.F., 04510, Mexico
Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edif. No. 9 U.P. Zacatenco, México D.F., 07738, Mexico
Departments of Physics and Psychology, Queens College, City University of New York, 65-30 Kissena Boulevard, SB B322, Flushing, NY 11367, USA
Adjunct Senior Research Scholar, Advanced Consortium on Cooperation, Conflict, and Complexity (AC4), Earth Institute, Columbia University, New York, NY 10027, USA
Physics Program, The Graduate Center, City University of New York, New York, NY 10016, USA
Author to whom correspondence should be addressed.
Academic Editor: J. A. Tenreiro Machado
Entropy 2015, 17(11), 7798-7810;
Received: 27 August 2015 / Revised: 12 November 2015 / Accepted: 13 November 2015 / Published: 20 November 2015
(This article belongs to the Section Complexity)
PDF [397 KB, uploaded 20 November 2015]


We study the correlation properties of word lengths in large texts from 30 ebooks in the English language from the Gutenberg Project ( using the natural visibility graph method (NVG). NVG converts a time series into a graph and then analyzes its graph properties. First, the original sequence of words is transformed into a sequence of values containing the length of each word, and then, it is integrated. Next, we apply the NVG to the integrated word-length series and construct the network. We show that the degree distribution of that network follows a power law, P ( k ) ∼ k - γ , with two regimes, which are characterized by the exponents γ s ≈ 1 . 7 (at short degree scales) and γ l ≈ 1 . 3 (at large degree scales). This suggests that word lengths are much more strongly correlated at large distances between words than at short distances between words. That finding is also supported by the detrended fluctuation analysis (DFA) and recurrence time distribution. These results provide new information about the universal characteristics of the structure of written texts beyond that given by word frequencies. View Full-Text
Keywords: words frequency; words recurrence; syllables; texts words frequency; words recurrence; syllables; texts

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Guzmán-Vargas, L.; Obregón-Quintana, B.; Aguilar-Velázquez, D.; Hernández-Pérez, R.; Liebovitch, L.S. Word-Length Correlations and Memory in Large Texts: A Visibility Network Analysis. Entropy 2015, 17, 7798-7810.

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