A Co-occurrence Network Approach To Analyzing Chinese Modern Poems And English Poems

In 1960s, Erdos and Renyi established their famous ER random graph model, which is the start of systematic studies on complex networks. In 1998, Watts and Strogatz created the WS model which cnloscs the'small-world' feature exhibited in many realistic networks. In 1999, Barabasi and Albert[2] formulated the BA model with a power-law degree distribution. Since then, numerous studies in complex networks have been conducted by researchers from natural sciences, social sciences, and engineering technology fields.[3-9]In 1999, Faloutsos et al.[10]found that their Internet models arc scalc-frcc and the eigenvalues of their adjacency matrices have power-law distributions. Since then, several researches on realistic networks [11-13] showed that in a lot of scalc-frcc networks the corresponding adjacency matrices have power-law eigenvalue distributions. In 2001, Farkas ct al. [14]studied the spectral densities of the adjacency matrices of ER random graphs, the BA model and the WS model. After that, researchers investigated some other realistic networks and got rich results [15-16].Human languages can be viewed as a complex adaptive system formed by a long-time evolution [17]. Cancho and Sole [18]brought the method of com-plex networks into the study of human languages in 2001. In their paper, the co-occurrence network considered is small-world and scale free. Since then, re-searchers worked on several different languages by generating networks using different methods at different levels. Following are main network generating methods in use:co-occurrence [18,19], syntax [20,21], semantics [22,23] or concep-tion [24. There arc also several researches on Chinese language networks [25-32]. We I33-34] introduced for the first time the idea, of generating networks for each single articles, and investigated single character and word co-occurrence networks of articles from four styles of modern Chinese and English (essays, novels, popular scientific articles, news reports). Following this direction, in 2010, we investigated co-occurrence character networks of Chinese prose ar-ticles from different periods and studied language evolution from a complex-network viewpoint[35].However, there arc only a few results on spectral analysis of adjacency matrices of language networks. In 2002, Bclkin et al. [36]studied the spec-tral properties of the Laplace matrices of their network models for English and French languages. In 2009, Mukhcrjcc et al.[37]analyzed spectral densi-ties and eigenvalue distributions of the adjacency matrices of their phonetic networks. In 2010, Choudhury et al.[38] conducted research on spectral densi-ties of adjacency matrices of co-occurrence networks in English, French, and other languages. Yet, there has been no spectral result for Chinese language networks.Various forms of the old English rhymes were completed and fixed in the 15-16th centuries. English free verses developed in the 18th century. During this period, the old English rhymes made changes under the impact of free verses and evolved into the so-called new English rhymes. Meanwhile, led by great writers in the 19th century, English prose poems quickly rose and finally caused the nowadays situation where free verses, new rhymes, and prose poems form the three pillars of modern English poetry [39,40].After 1919, Chinese poets experimented on combining the techniques from both poems in foreign languages and ancient Chinese poems, and finally cre-ated the modern Chinese poetry, including three main styles, modern rhymes (abbreviated as rhymes in the following), free verses, and prose poems [41]. Al-though poems of foreign languages have served as an important resource for the formulation of styles of modern Chinese poems, modern Chinese poems have quite different linguistic properties from those of foreign poems. Previ-ous researchers, from a pure literature point of view, have obtained rich results in the study of the similarities and differences between modern Chinese poems and English poems [42-50]. In this article, we study Chinese and English poems from the approach of complex networks. By investigating degree distributions and other statistics, as well as the spectra of adjacency matrices of networks, we analyze the features and differences of Chinese and English poem networks. This article consists of four chapters, described as follows.In Chapter 1, we introduce basic concepts of complex networks, the sclcc-tion of Chinese and English poems, the segmenting of Chinese words, and the method of generating co-occurrence networks for Chinese and English poems.In Chapter 2, we study degree distributions, average shortest path lengths and clustering coefficients of 600 single Chinese poem networks, and find that 98.5% networks have scale-free property and only 80% networks have the small world effect, especially only 51% prose poem networks have the small world effect. Also interesting is that the clustering coefficients in some poem net-works arc 0. We also study hierarchical organizations, assortativencss, spectral density, and spectral distribution of adjacency matrices for these three types of Chinese poem networks. We find that different rhymes and poetic styles lead to differences in statistical parameters.In Chapter 3, we study degree distributions, average shortest path lengths, and clustering coefficients of 400 single English poem networks, and find that 87.5% networks arc scale-free and 93.2% networks have small-world effect. In addition, we study hierarchical organizations, assortativeness, spectral density, and spectral distributions of adjacency matrices for these four types of English poem networks. We explain these results with analysis of the writing charac-teristics of different kinds of poems, and try to explain these differences from linguistic approach.In Chapter 4, through analyzing and comparing statistics of Chinese and English poem networks, we find that Chinese and English single poem networks differentiate in the portion of networks with the scale-free property while in av-erage they have similar power-law exponents; Chinese and English single poem networks have different portions with respect to small-world effect and differ-ent average shortest path lengths and clustering coefficients; for English single poem networks, the portion with hierarchical organizations is much smaller than that of corresponding types of Chinese poems, and their assortativeness are slightly different. Moreover, both Chinese and English combined poem net- works arc scale-frcc, small-world and disassortative networks with hierarchical organizations, but differentiate in specific statistics.