Translating Networks Assessing Correspondence Between Network Visualisation and Analytics

Network interpretation is a widespread practice in the digital humanities, and its exercise is surprisingly flexible. While there is now a wide variety of uses in different fields from social network analysis (Ables et al., 2017) to the study of document circulation metadata (Grandjean, 2016) or literature and linguistic data (Maryl and Elder, 2017), many projects highlight the difficulty of bringing graph theory and their discipline into dialogue. Fortunately, the development of accessible software (Bastian et al., 2009), followed by new interfaces (Rosa Pérez et al., 2018; Wieneke et al., 2016), sometimes with an educational dimension (Beaulieu, 2017; Xanthos et al., 2016), has been accompanied in recent years by a critical reflection on our practices (Weingart, 2011; Kaufman et al., 2017), particularly with regard to visualisation. Yet, it often focuses on technical aspects.
In this paper, we propose to shift this emphasis and address the question of the researcher’s interpretative journey from visualisation to metrics resulting from the network structure. Often addressed in relation to graphical representation, when it is not used only as an illustration, the subjectivity of translation is all the more important when it comes to interpreting structural metrics. But these two things are closely related. To separate metrics from visualisation would be to forget that two historical examples of network representation, Euler (1736) and Moreno (1934), are not limited to a graphic reading (the term “network” itself would only appear in 1954 in Barnes’ work). In the first case, the demonstration was based on a degree centrality measurement whereas in the second case the author made the difference between “stars” and “unchosen” individuals while qualifying the edges as inbound and outbound relationships.
This is why this paper propose to examine the practice of visual reading and metrics-based analysis in a correspondence table that clarifies the subjectivity of the translation while presenting possible and generic interpretation scenarios.

Visual approach: making the global structure readable
The way we read networks has changed over time. Historically the question of network readability was asked in terms of aesthetic criteria. In the word of Jacob Moreno “the fewer the number of lines crossing, the better the sociogram”. Even in the nineties, when giving birth to the modern layout algorithm, Früchterman and Reingold (1991) aimed at “minimizing edge crossings” and “reflecting inherent symmetry”. However these criteria do not seem so crucial to practices observed nowadays in digital humanities (and beyond).

Fig. 1 Different contexts for network visualisation in DH2016, DH2017 and DH2018 abstracts.

Looking at recent papers in digital humanities, networks appear to have a wide range of usages. Their visualisations are either self-sufficient [fig. 1.a.] (Algee-Hewitt, 2018; Pino-Diaz and Fiormonte, 2018; Verhoeven et al., 2018; Marraccini, 2017), an optional help to understanding [fig 1.b.] (Colavizza et al., 2016) or strongly connected to the text. Some authors use them to highlight the position of a specific node [fig. 1.c.] (Moretti et al., 2016), to compare layouts [fig. 1.d.] (Sozinova, 2016) or the layout of the same graph in time [fig. 1.e.] (Wright, 2016). They may aim at visualising communities [fig. 1.f.] (Rybicki et al., 2018; Torres-Yepez and Zreik, 2018), mapping a general structure [fig. 1.g.] (Gao et al., 2017), tracking density patterns [fig. 1.h.] (Gao et al., 2018) or monitoring algorithms like modularity clustering [fig. 1.i.] (Choinski and Rybicki, 2017). These usages reveal a different perspective in network visualisation where we expect the visual to translate underlying relational structures.
It helps to give different names to these two different approaches. We call
diagrammatic the perspective where the network is a diagram that we read by following paths. We do not want the edges to cross and we use aesthetic criteria to bring clarity. It was Moreno’s perspective, and is still relevant to small networks and local exploration. Then we call
topological the perspective where the network is a structure that we read by detecting patterns. We expect the visualisation to help us retrieve structural features like clustering or centralities. It is a common practice in digital humanities, more holistic and relevant to larger networks. Aside or in complement, classic data visualisation is also employed to visualise non-relational structures (node attributes, etc.).

Fig. 2 Various layouts do not follow a force-driven algorithm to make non-relational dimensions of the data explicit.

In the topological perspective, a standard procedure is to assign nodes a position using a force-driven algorithm. This family of algorithms is known for displaying clusters that match a widely used measure of community detection, modularity clustering (Noack, 2009). Its translation remains however difficult to interpret locally, as we can never give a simple explanation for a node’s position. Classic data visualisation also translates non-relational structures, by itself or combined with a relational perspective. Different structural features may require different visualisations: the examples of fig. 2 shows curated visualisations using categories [fig. 2.a boys and girls, in the famous example of (Moreno, 1934)], temporality [fig. 2.b] (Jänicke and Focht, 2017) or hierarchy [fig. 2.c] (Grandjean, 2017). Though very different from force-driven placement, they display better certain structural features.

Objectifying the structure with metrics
Often opposed to visual interpretation, of which they would be a more objective and reliable representation, centrality measures have a history that goes back to more than half a century and shows that they are not immutable and require constant adaptation to usage Moreover, Freeman (1979) insists on the fact that the notion of “centrality” is the result of several intuitive conceptions. To remind that these metrics are based on “intuition” means to recognize that they have no meaning in themselves and that their interpretation must be rediscussed - and therefore translated - according to the context. This paper thus proposes to list and evaluate to which extent these metrics are applicable to humanities and social science data and can, if necessary, be “translated” into this language to complement visual analyses.

Fig. 3 Three levels of interpretation that can be articulated: visual analysis (examples top left), use of global metrics (examples bottom right) and use of local metrics (highlighted nodes).

Global properties
Statistical analysis allows for comparing networks across multiple dimensions at once (Tank and Chen, 2017). For instance, comparing the
number of nodes and edges of different graphs of the same type (Trilcke et al., 2016) can be a ranking tool that is directly translatable into natural language. In addition to that, studies suggest that
density (the number of edges in relation to the number of nodes) is relevant to analyse character networks, especially when compared within a homogeneous collection (Evalyn and Gauch, 2018; Grandjean, 2015). This is also the case when measuring
average path length (Trilcke et al., 2016).

Local properties
With regard to local measures, the
degree (number of neighbouring nodes) is the simplest
centrality, and the only one systematically used between the late 1950s and early 1970s, before the development of more diversified metrics (Freeman, 1979). Its simplicity allows for a transparent translation: in a literary network, for example, it counts the number of times one character speaks to another (Jannidis et al., 2016).

The notion of
betweenness centrality disrupts the conception of what the “centre” of a network may consist of. Its ability to reveal structural elements bridging large, immediately visible clusters makes it popular in the social sciences since the emergence of Granovetter’s concept of “weak ties” (Granovetter, 1973). Betweenness is very closely linked to the notion of circulation: it counts the shortest paths to detect intermediate “bridges” or “key passages” capable of opening or locking certain parts of the network (Tayler and Neugebauer, 2018). Depending on applications, these are therefore both positions of power and vulnerable places.

The
closeness centrality allows to highlight the “geographical” middle of the graph. In networks of a certain density and when they are not divided into several distinct communities, the closeness is generally fairly evenly distributed and allows a good translation of the notions of “center” and “periphery”.

For its part, the
eigenvector centrality is quite complicated to translate since it works iteratively and is very much dependent on the structural context at short and medium range around a node. “Prestige” or “influence” centrality, named “power” centrality by its author (Bonacich, 1972), it qualifies a node’s environment while operating in cascade: a well connected node gives its neighbours a part of its authority capital, and so on. It is therefore particularly useful when trying to analyze the hierarchy of the nodes in a graph (Piper et al., 2017). The most well-known use of this measure is the backbone of the Google search engine: the PageRank algorithm (Brin and Page, 1998).

Towards mixed approaches
This contribution proposes a table of correspondence between the concepts of graph theory and the practice of visual network analysis in the social science and humanities. This effort must not be understood as a demarcationist attempt at telling the right method from the wrong. The “dictionary” is not exhaustive and only aims at helping to bridge two worlds that have more in common that what meets the eye. By focusing on translating methods, we want to stress that crossing points are real even though they do not come without issues, and thus require our methodological attention.
We also note that the analysis should not be limited to a catalogue of well-known methods (basic centralities, etc.) but that approaches combining several of those should be encouraged to obtain an optimal and innovative “translation”. In this way, we could compare metrics (Escobar and Schauf, 2018) or combine them to establish rankings (Fischer et al., 2018; Grandjean, 2018: 328). Furthermore, the enrichment of the networks by means of categories that are not dependent on the structure, like the gender of individuals in a social network (Dunst and Hartel, 2017) or the discipline of projects in a scientometric analysis (Grandjean et al., 2017), allows to test translation and interpretation hypotheses by avoiding the blind approach of testing all possible graph metrics.

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