## 2 Preliminaries and Literature Review
### Character Networks and Plot Structures  
According to [PERSON] [14], stories are developed by interactions between protagonists and their surrounding characters. From this intuition, various studies [2; 3; 4; 5; 6; 9; 26] have attempted to model and analyze stories based on the social networks of characters that have appeared in the stories. Nodes of the social networks are characters, and edges represent interactions between the characters. We call these social networks of characters 'character networks'. Since narrative works and stories are time-sequential, the existing studies [6; 9; 27] have defined the character network as a dynamic social network. They attempted to analyze stories' development based on how character networks dynamically evolve. The dynamic character network is made by segmenting narrative works into regular units (e.g., scenes) and composing character networks on each unit. We can choose an appropriate unit by considering (i) media and formats of narrative works and (ii) tasks that we deal with (e.g., recommendation, indexing, and summarization). For example, according to narratology studies [17; 28], a movie consists of 3 to 4 acts, an act consists of 3 to 6 sequences, and a sequence consists of 2 to 5 scenes. This study employs the scene as the regular unit since there have not been methods for automatically discovering acts or sequences from visual narrative works with enough accuracy, to the extent of our knowledge [29; 30; 31; 32; 33; 34; 35]. The character network has been defined as follows:  
**Definition 1** (Character Network [9; 10]). : _Suppose that \(N\) is the number of characters that appeared in the \(a\)-th narrative work, \(\mathbb{C}_{a}\). When \(N(\mathbb{C}_{a})\) indicates a character network of \(\mathbb{C}_{a}\), and \(\mathbb{R}\) refers to the real number, \(N(\mathbb{C}_{a})\) can be defined as a matrix \(\in\mathbb{R}^{N\times N}\). Each component of \(N(\mathbb{C}_{a})\) indicates a degree of proximity between two characters._  
_By segmenting \(\mathbb{C}_{a}\), we transform \(N(\mathbb{C}_{a})\) into a dynamic social network. When \(\mathbb{C}_{a}\) includes \(L\) scenes, \(s_{a,l}\) is the \(l\)-th scene of \(\mathbb{C}_{a}\), and \(N(s_{a,l})\) indicates a character network only within \(s_{a,l}\), a relationship between \(N(\mathbb{C}_{a})\) and \(N(s_{a,l})\) can be formulated as:_  
\[N(\mathbb{C}_{a})=\sum_{l=1}^{L}N(s_{a,l})= \begin{bmatrix}a_{1,1}&\cdots&a_{1,N}\\ \vdots&\ddots&\vdots\\ a_{N,1}&\cdots&a_{N,N}\end{bmatrix} ,\ \ \mathbb{C}_{a}=\big{<}s_{a,1},\cdots,s_{a,l}, \cdots,s_{a,L}\big{>}, \tag{1}\]  
_where \(a_{ij}\) indicates proximity of \(c_{i}\) for \(c_{j}\) when \(c_{i}\) is the \(i\)-th character that appeared in \(\mathbb{C}_{a}\)._  
For composing character networks and measuring proximity, various methods and models have been proposed [2; 3; 4; 5; 6; 9; 26; 37; 38; 39]. In this study, we use lingual character networks proposed by [PERSON] and [PERSON] [9]. This model estimates the proximity, based on dialogue frequency between characters, similar to the conventional models [3; 15; 24; 40]. However, it can measure the proximity more accurately by considering that a scene can contain multiple conversations. Thus, while the existing dialogue-based character networkssuppose that all characters in a scene are listeners of all dialogues spoken in the scene, we limit listeners into participants of each conversation. [PERSON] and [PERSON] [9] also compared various character network models. This comparison lets us know that participating in conversations is a significant feature by itself. Thus, we consider the number of dialogues and conversations that each character is involved in. In addition, not only frequency of dialogues but also lengths of dialogues are meaningful for analyzing story flow, especially in major event detection [41]. Thus, we also annotate the number of words in dialogues on character networks.