# From Discourse Relations to Network Edges: A Network Theory Approach to Discourse Analysis
## 1 Introduction  
One of the main research goals in computational theories of discourse structure has been to reveal whether there are specific discourse coherence patterns followed by speakers in single-author texts, monologues and dialogues that could be exploited for building NLP applications ([1; 2; 3; 4; 5; 6]). Being able to answer this question allows to also address another question of bigger theoretical depth and importance, namely how coherence and cohesion are realized in the discourse. Exploring discourse relations remains a topic of growing interest, and several rather sophisticated approaches have recently been proposed [7; 8; 9; 10; 11; 12]. The current trend in attempting to answer this and similar questions in NLP in general has been to train Transformer models ([13; 14; 15]) and construct the so-called probing tasks to indirectly obtain a deeper understanding of discourse coherence and cohesion. However, it still does not seem feasible to extract interpretable semantic properties of the discourse out of these deep learning models, and one can still use some valuable lessons from the formal discourse semantic tradition in order to achieve this ([16; 17; 18; 19; 20; 21; 22; 23; 24; 25]). In this paper, we intend to focus on three different types of recorded discourse-annotated data spanning two languages, English and Greek: (a) the single-author written texts of two daily newspapers with large circulation in Greece that were included in the corpus C58 ([26]) and (b) the multiparty dialogue texts of the STAC corpus annotated in two stages, resulting in two discourse-annotated versions; (i) the first version includes chat logs (or chat moves) recorded in a virtual environment during an online game session ([27; 28; 29], and (ii) the second version includes the same multipartydialogues accompanied by the messages automatically generated by the game software. These messages describe the nonlinguistic events that take place during a game session and thus _situate_ the linguistic utterances in the broader nonlinguistic context of usage. The availability of discourse-annotated corpora allows us to use quantitative methods to pin down the essence of discourse coherence and cohesion but also to profit from the numerous tools provided by the mathematical field of network analysis ([30; 31; 32]). Existing formal discourse theories have been providing the formal means to construct discourse representations that can be mapped to networks that reflect the information flow of discourse and reveal hidden properties of the discourse. Network edges play a crucial role in a discourse dialogue network. They represent the connections or relationships between different discourse units, such as utterances or events, within the network. The importance of network edges lies in their ability to capture the flow and dynamics of discourse interactions. Most notably, network edges provide a pathway for the exchange of information and meaning between discourse units. They indicate how different units are connected and how information is transmitted within the discourse. By following the network edges, one can trace the progression of ideas, arguments, or conversations in the discourse dialogue. The discovery of significant network patterns in the discourse representations of the corpora would suggest that the speakers engage in discourse by following implicit strategies, and this might mean that speech acts are related in predictable ways. Moreover, traceable differences and commonalities in the network patterns of single-author written texts and multiparty dialogue texts, as well as between different languages, would help formulate theoretically driven corollaries related to different discourse types. Based on two corpora and the three datasets that accompany them, the network analysis that we provide gives important and counter-intuitive insights to speakers' preferences in constructing and interpreting discourse structure.