Compactified Horizontal Visibility Graph for the Language Network

A compactified horizontal visibility graph for the language network is proposed. It was found that the networks constructed in such way are scale free, and have a property that among the nodes with largest degrees there are words that determine not only a text structure communication, but also its informational structure. Construction of networks with text elements, words, phrases or fragments of natural language as nodes in some cases allows to detect the structural elements of the text critical for its connected structure and find informationally significant elements, as well as words that are secondary for understanding of the text. Such networks may also be used to identify unconventional text components, such as collocations, supra-phrasal units [1], as well as for finding similar fragments in different texts [2]. There is a multitude of approaches to constructing networks from the texts (so-called language networks) and different ways of interpreting nodes and links, which causes, accordingly, different representation of such networks. Nodes are connected if corresponding words are either adjacent in the text [3, 4], or are in a single sentence [5], or are syntactically [6, 7] or semantically [8, 9] connected. At the intersection of digital signal processing (DSP) theory and complex network theory there are several ways of constructing networks from the time series, among those are visibility graph construction methods (see survey [10]), namely the horizontal visibility graph (HVG) [11,12]. Based on these approaches, networks can also be constructed from texts in which numeric values are assigned in some manner to each word or phrase. The examples of functions assigning a number to a word are: ordinal number of a unique word in a text, length of the word, " weight " of the word in a text, e.g., generally accepted TFIDF metric (canonically, a product of the term frequency in a text fragment and a