Network properties of written human language

We investigate the nature of written human language within the framework of complex network theory. In particular, we analyze the topology of Orwell’s 1984 focusing on the local properties of the network, such as the properties of the nearest neighbors and the clustering coefficient. We find a composite power law behavior for both the average nearest neighbor’s degree and average clustering coefficient as a function of the vertex degree. This implies the existence of different functional classes of vertices. Furthermore, we find that the second order vertex correlations are an essential component of the network architecture. To model our empirical results we extend a previously introduced model for language due to Dorogovtsev and Mendes. We propose an accelerated growing network model that contains three growth mechanisms: linear preferential attachment, local preferential attachment, and the random growth of a predetermined small finite subset of initial vertices. We find that with these elementary stochastic rules we are able to produce a network showing syntacticlike structures.

Figure 1

Illustration of the language network for the first 60 words of Orwell’s 1984.

Figure 2

(a) Measure of Zipf’s law on 1984. The dashed line is a power law with slope $-1.1$. (b) The degree distribution $P\left(k\right)$ measured on the same novel. The slope found is $-1.9$.

Figure 3

The clustering coefficient against the degree of the vertices in 1984.

Figure 4

(a) The average clustering coefficient as a function of the vertex degree. (b) The average nearest neighbor degree as a function of the vertex degree. Noise has been removed using logarithmic binning. In both plots two different regions emerge displaying different power law behavior.

Figure 5

(a) Number of occurrences of repeated binary structures of words in the text against the total number of words. (b) Number of occurrences of previously existing words in the text, that are not part of previously existing binary structures, against the total number of words.

Figure 6

(a) Count of the occurrence of binary structures during the evolution of the network for the D-M model compared to the real network data. (b) Probability distribution for the occurrence of some of the most frequent words in 1984. To obtain this measure we partitioned the novel, each partition of 500 words, and counted the number of times $n$ that each word appears in each partition. As we can see different words display different distributions. In particular “the” and the “full stop,” that are structural words, display a Gaussian distribution, as shown by the Gaussian fits in the figure. Otherwise a word such as “Winston,” who is the first character in the novel, and is a meaningful word, or the pronoun “he” follow different distributions.

Figure 7

Comparison between the D-M model, Model 3, and real data. (a) Zipf’s law. (b) Degree frequency count. In both plots logarithmic binning is used to reduce noise.

Figure 8

Average clustering coefficient versus the degree of the vertices. (a) Comparison between D-M model and real data. (b) Comparison between Model 3 and real data.

Figure 9

Comparison of the average clustering coefficient versus the degree of the vertices, obtained using logarithmic binning, between real data, D-M model and Model 3.