Arts, Humanities and Complex Networks

Representing networks is a major interest of researchers in information visualization. In this article, The authors present novel visualization techniques based on Jacques Bertin’s reorderable matrices. As the human brain is particularly effective at processing visual information, researchers in computer science have developed a number of visual exploration systems to analyze graphs and networks. In the last five years, massive online social networks became available for scientists to analyze, pushing researchers to innovate in the field of graph visualization. In this article, I present recent techniques designed to visualize large and dense social networks based on Jacques Bertin’s reorderable matrices. Node-Link Diagrams Node-link diagrams are the most commonly used representations of graphs and networks. It is well illustrated by Freeman in his survey and history of social network visualization [1]. In this article, Freeman presents a wide variety of social networks and demonstrates that visual representations are a powerful tool to illustrate social network analysis concepts such as central actors or communities. Figure 1 demonstrates how this visual representation can depict two communities as dense groups of nodes and links and places the actors bridging them in the center of the diagram. Node-link representations are widely used and familiar to a very large audience, making them a powerful communication tool. However, their readability and the message they convey greatly depends on the positions of their nodes. Since the 1990s, an entire field of research is devoted to the problem of graph drawing, i.e. generating algorithms to place nodes in the space [2]. Scaling to large networks with several thousand or even millions of nodes remains a challenge. Node-link diagrams with more than a few hundred nodes often become an undistinguishable pile of nodes and links, difficult to transform either automatically or manually into a readable representation. A common solution consists in filtering data. However, when removing nodes and links, the topological structure of the network may be damaged and properties lost. For these reasons, researchers such as Jacques Bertin investigated an alternative representation: the matrix. Matrix Representations In The Semiology of Graphics [3], Jaques Bertin shows that replacing numerical values by visual indicators and reordering rows and columns dramatically improves the readability of tables and matrices. Figure 2 shows an example of the reorderable matrix, representing the production of 5 types of meat in 5 countries. While the numerical table makes it possible to read any value, it remains difficult to grasp higher-level insights about this data. However, once values are transformed into graphical indicators and rows and columns reordered, one can discover more insights about the data. For example, an analyst can quickly spot three different profiles of production (marked A, B and C in the figure) and identify that France has the highest production overall. A critical element of the readability of this matrix is its ordering. Reordered matrices provide opportunities to discover more insights about the data than unordered ones. Many reordering algorithms exist, ranging from graph linearization algorithms in graph theory to microarray clustering algorithms in bioinformatics. While empirical evidence shows that different reordering algorithms make different patterns emerge in the data, assessing their quality remains an open question. Graphs as Matrices In a matrix representation of a graph, vertices are placed both in rows and columns. If two vertices are connected, the corresponding cell of the table is marked. Since vertices are represented both in rows and columns, two cells correspond to a pair of vertices, making it possible to represent directed edges. This type of matrix is an adjacency matrix. Adjacency matrices are particularly useful for dense or large networks. Their representation does not degrade as drastically in visual clutter (e.g. edge crossing) and remains efficient to display on screen. Indeed, the cells representing the links do not cross by overlapping each other, and the time needed to draw the representation is low since the whole list of actors is placed linearly. However, matrices use a large amount of space since they represent all possible pairs of vertices. A user study [4] also showed that path-related tasks (e.g. find the shortest path between two vertices) are difficult. My research explored the design of hybrid representations and novel interaction techniques to alleviate these drawbacks [5]. Fig. 2. Numerical table of the production of 5 types of meat by 5 countries (left) and visual matrix with rows and columns reordered (right). (© Nathalie Riche) A