Core-Periphery Organization of Graphemes in Written Sequences: Decreasing Positional Rigidity with Increasing Core Order

Abstract

The positional rigidity of graphemes (as well as words considered as single units) in written sequences has been analyzed in this paper using complex network methodology. In particular, the information about adjacent co-occurrence of graphemes in a corpus has been used to construct a network, where the nodes represent the distinct signs used. Core-periphery structure of this network has been uncovered using k-core decomposition technique suitably generalized for directed networks. This allows identification of a core signary or “graphem-ome” of the corresponding writing system, i.e., the group of frequently co-occurring graphemes. The distribution of the frequency with which such signs occur at different positions in a sequence (e.g., at the beginning or at the end or in the middle) shows that while signs belonging to the periphery often occur only at specific positions, those in the innermost cores may occur at many different positions. This is quantified by using a positional entropy measure that shows a systematic increase with core order for the different databases used in this study (corpus of English, Chinese and Sumerian sentences as well as a database of Indus civilization inscriptions).