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

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Unidad Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, Av. IPN No. 2580, L. Ticomán, México D.F., 07340, Mexico
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Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edif. No. 9 U.P. Zacatenco, México D.F., 07738, Mexico
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Departments of Physics and Psychology, Queens College, City University of New York, 65-30 Kissena Boulevard, SB B322, Flushing, NY 11367, USA
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Adjunct Senior Research Scholar, Advanced Consortium on Cooperation, Conflict, and Complexity (AC4), Earth Institute, Columbia University, New York, NY 10027, USA
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Physics Program, The Graduate Center, City University of New York, New York, NY 10016, USA
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Author to whom correspondence should be addressed.
Entropy 2015, 17(11), 7798-7810; https://doi.org/10.3390/e17117798
Received: 27 August 2015 / Revised: 12 November 2015 / Accepted: 13 November 2015 / Published: 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 (www.gutenberg.org) 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
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MDPI and ACS Style

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. https://doi.org/10.3390/e17117798

AMA Style

Guzmán-Vargas L, Obregón-Quintana B, Aguilar-Velázquez D, Hernández-Pérez R, Liebovitch LS. Word-Length Correlations and Memory in Large Texts: A Visibility Network Analysis. Entropy. 2015; 17(11):7798-7810. https://doi.org/10.3390/e17117798

Chicago/Turabian Style

Guzmán-Vargas, Lev; Obregón-Quintana, Bibiana; Aguilar-Velázquez, Daniel; Hernández-Pérez, Ricardo; Liebovitch, Larry S. 2015. "Word-Length Correlations and Memory in Large Texts: A Visibility Network Analysis" Entropy 17, no. 11: 7798-7810. https://doi.org/10.3390/e17117798

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