Network Dynamics, Plot Analysis: Approaching the Progressive Structuration of Literary Texts

Introduction and related works
In recent years, the application of network analysis methods to literary texts has evolved into an independent research field of digital literary studies. Methods for the automated extraction of network data (named entity recognition, co-reference resolution) and their evaluation are of particular importance (El-son et al. 2010; Park et al. 2013; Agrarwal et al. 2013; Fischer et al. 2015; Waumans et al. 2015; Jannidis et al. 2016). Based on the data obtained, several types of analyses were developed: an empirical, quantitative and hierarchical description of literary characters (Jannidis et al. 2016), corpus-based analyses exploring options for historical periodisation of literature (Trilcke et al. 2015) and types of aesthetic modelling of social formations in and by literary texts (Stiller et al. 2003; Stiller & Hudson 2005; Trilcke et al. 2016).

What has been neglected so far (although already suggested by Moretti 2011) is the application of network analysis as a tool for quantitative plot analysis. In fact, current approaches in the field of literary network analysis are not suited to gaining insights into the plot development of literary texts (Prado et al. 2016). The sequential dimension of literary texts, as a consequence of their temporality, usually remains in the dark: what is extracted, visualised and analysed

are static networks. Plot, however, is essentially a concept supposed to theoretically encompass the temporality of narrative (as well as dramatic) texts: "the repeated attempts to redefine parameters of plot reflect both the centrality and the complexity of the temporal dimension of narrative" (Dannenberg 2005: pp. 435). Plot can be understood as a concept for the description of the "progressive structuration" (Kukkonen 2013: §4) of literary texts.

Research objective: plot analysis
Attempts to further develop literary network analysis towards a quantitative plot analysis must consider the temporal dimension in the modelling of their research objects. The structure of a literary text is to be modelled as a changing sequence of network states. It is only through looking into these network dynamics that we can discuss network-analytic approaches for a quantitative plot analysis.

Following Prado et al. 2016, we are currently extending our research on literary networks (Trilcke 2013; Fischer et al. 2015ff.; Fischer et al. 2015; Trilcke et al. 2016) to the analysis of progressive structuration. Our goal is to examine whether (and with what kind of limitations) we can flesh out an operationalisation for the plot analysis of literary texts. By doing so, we are, of course, not trying to replace the semantically rich and versatile concept of 'plot' with a quantitative and thus reductionist concept. Rather, we will show that certain aspects of what is commonly discussed within the framework of plot analysis can be retraced by means of a computer-based analysis of network dynamics.

The visualisation of dynamic graphs, as is common in other domains (Pohl et al. 2008; Frederico et al. 2011), has recently been transferred to literary networks (Xanthos et al. 2016). While it may come in useful when close-reading a text and for didactic purposes, it is unsatisfactory when it comes to an actual corpus-based analysis. There are no canonical methods to help us compare network visualisations generated automatically by force-directed graph drawing algorithms. The reception of dynamic visualisations just does not offer practical analytical means. From a dedicated distant-reading kind of perspective, the calculation of dynamic network metrics and their statistical processing is much more promising as it offers options to describe general characteristics of networks from a larger corpus as well as to compare specific formal types of networks within the corpus.

Measuring dynamic literary networks
A number of basic global measures for the analysis of dynamic networks (i.e., size, density, homogeneity in the distribution of ties, rate of changes in nodes, rate

of changes in ties) has been discussed by Carley (2003:

pp. 135-36). In addition, Prado et al. 2016 recently suggested the application of actor-oriented measures, especially centrality indices, for the reconstruction of plot development. We are currently applying these measures to our own corpus, consisting of 465 German language plays. We also developed a set of other measures with recourse to traditional theoretical concepts for the description of specific phenomena of plot development, especially with regard to types of dramatic expositions (Pfister 1977: pp. 124-36), the "classical" act structure of tragedy and the composition principle of main and secondary plots (Pfister 1977: pp. 286-89). Calculation of these measures was implemented in our own network analysis tool drama-vis (Kittel/Fischer 2017).

Event-based measures
In general, two types of measures can be distinguished for describing dramatic texts as dynamic networks: event-based and progression-based measures. Event-based measures are used to identify or characterise a particular point in time within a drama. In this context we developed an all-in index, a value that identifies the point in time at which all characters have occurred at least once in a drama (see Figure 1).

Figure 1 : All-in index for 6 selected plays

The final-scene-size value characterises a specific point in time, in this case the last scene of a drama. It determines the percentage of all characters of a drama which appear on stage in the last scene. This value shows characteristic differences between dramatic subgenres, especially when comparing tragedies and comedies (see Figure 2).

Figure 2: Final-scene-size index (mean values of entire corpus and subgenres)

Progression-based measures
While event-based measures allow assumptions about a particular state/point in time of the dynamic network, progression-based measures allow a general characterisation of the transformation of a dramatic network. In this regard, we introduced a measure we call the drama-change rate. The basis of our calculation is a modified Levenshtein distance, which only takes into account insertions ("add character") and deletions ("delete character"). In each case, we compare characters present in two consecutive scenes, eventually resulting in what we call the segment-change rate (Figure 3).

Scene 1 2 3 4 Scene 12 3

segment change rate segment change rate

» 1/2 = 0.5 =2/3 = 0.66

Figure 3: Calculation of the segment-change rate (example)

BI

The sum of all segment-change rates of a drama divided by the number of all segment-change rates is what we call the drama-change rate. The development of this rate can be represented in a chart, which due to its shape we tentatively called the beat chart (Figure 4).

Figure 4: Beat chart for Goethe's play "Iphigenie auf Tauris" (1787)

Having calculated the drama-change-rate value for the entire corpus, we can start to compare a larger set of dramas with each other (Figure 5). It becomes evident that our corpus does not exhibit a clear trend along the timeline. Instead, we witness the emergence of characteristic types of dramas, which differ characteristically from the other texts in our corpus.

Figure 5: Historical distribution of drama-change rates in the DLINA corpus

On the one hand, we can identify dramas exhibiting a

high drama-change rate, i.e., highly dynamic dramas with a constant alternation of characters on stage (Figure 6). On the other hand, low-dynamic dramas can be

Figure 6: Two examples of highly dynamic dramas - left: Goethe's "Egmont" (1788); right: Lenz's "Der Hofmeister" (1774)

Figure 7: Two Examples for low-dynamic dramas - left: Goethe's "Der Burgergeneral" (1793), right: Rilke's "Ohne Gegenwart" (1898)

A further option for the comparative analysis of our oscillatory beat charts is the analysis of the standard deviation of all segment-change rates of a drama. We can again distinguish two particularly striking types: On the one hand, there are dramas with a high standard deviation, indicating that extensive changes of characters alternate with small changes; we can call them high-dynamic dramas (Figure 8). On the other hand, there are dramas showing a low standard deviation, so the change on stage takes place in the same rhythm, we call these texts low-dynamic dramas (Fig-

Figure 8: Two Examples for high-dynamic dramas - left: Benkowitz's "Die Jubelfeier der Hölle" (1801), right: Goethe's "Faust I" (1808)

Figure 9: Two Examples for low-dynamic dramas - left: Schnitzler's "Anatol" (1893), right: Schnitzler's "Der Reigen" (1902)

The preceding cases each describe characteristic deviations regarding the drama-change rate of groups of texts. In addition, a 'normal type' of drama can be identified, which corresponds to the mean value for the corpus both in terms of arithmetic mean and standard deviation (Figure 10).

Figure 10: Beat chart for Ganghofer's "Der Herrgottschnitzer von Ammergau" (1880)

It also appears that strong upward shifts, accompanied by a complete exchange of characters on stage, often coincide with act boundaries (vertical orange lines), which is in accordance with historical conventions of dramatic composition.

Summary and further research
Our research on dynamic networks provides basic components for a quantitative analysis of the progressive structuration of dramatic texts. Future research will have to develop and evaluate additional measures and it will be decisive to hold interpretations of these measures against the backdrop of historical drama poetics.

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